"Differentiate both sides of the equation V = Tr*with respect to t AP (using the chain rule on the right) to find a formula for dt

Q: Find an interval of definition for the equation x^2 dx/dt = 3x^3 t^2

A: Domain of definition is where X(t) is defined

Q: Part 4: A derivative computation using the FTC and the chain rule d d (F(2*)) = dx dt |3| e dx 20

A: Topic:- application of integration and derivatives

Q: Use the chain rule to differentiate f(t)=e^(4t sin(2t))

A: Let us take u=4tsin(2t) and f(t)=y, then we have y=e^u

Q: Consider a disease where immunity is lost. On average, after n days, a recovered person becomes…

A: Let t be the time ,which is an independent variable (measured in days). We have to take two related…

Q: Calculate the derivative e12x d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus.

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Q: Calculate the derivative d dx L In (t)dt using Part 2 of the Fundamental Theorem of Calculus.…

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Q: 4. Use the chain rule to find out the total derivative dv/dt, when v = xe/z, where r = t²,y = cos t,…

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Q: In the integration What is the implicit derivative of u? V9-4x² a. du = 2dx b. du = * - 2dx c. du =-…

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Q: D. Solve the differential equation using Laplace transform of y - 3y' + 2y = et ; when y(0) =0 and…

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Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y? + z²; x = psin o cos…

A: We have to find derivative of given function by using chain rule.

Q: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

A: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

Q: find the values of the derivatives ds/dt at t=0 if s = 2/(4 - t)

A: Given function is Differentiating with respect to t, we get

Q: 1. Find the total differential of the ff. at (1, -2).

A: The given function is f(x,y)=xy2-3y+2

Q: Calculate the derivative 10z d dz In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

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Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

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Q: Differentiate the following using chain rule Y = In (cot 3x – 2) Y = log cos? 3x

A: We need to find the derivative of Y=ln cot 3x-2 and Y=log cos23x. First problem: Now,…

Q: Find the derivative of the function. s=t° In t| ds dt

A: The solution is given below in the next step:

Q: Use Part 2 of the Fundamental Theorem of Calculus to find th. derivatives. dt sin y dy 1+ y? (b) dx…

A: Consider the integral ∫axfydy, where a is a constant. Note that, ∫axfydy will be a function in x.…

Q: d Use the Fundamental Theorem of Calculus to find the derivative. dx dt 1+ vE

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Q: Compute the derivative of g(x) = cos(t) dt-

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Q: S(«,9) =7+3y Also, find the total differential of the function.

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Q: Find the derivative of the function. s = t In |t| ds dt 11

A: The objective is to find the derivative.

Q: H (w) s (+リ? (outて)

A: The given problem is to find the inverse Fourier transform of the given function, we have to split…

Q: Find the differential dy of the given function. y = sec2x/(x2 + 1)

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Q: Calculate the derivative d dæ In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

A: First, we split the integral function into two terms. Now find the derivative of both integrals by…

Q: Find the general solution of the differential equa- tion / - a?y = -x - xy, %3D where |r| < 1.

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Q: Calculate the derivative 12x d dx In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

A: follow next step

Q: Given the function y = x* e* , find dty dx for x = -1. %3D

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Q: The delivery of an antibiotic through an intravenous line (IV) may be modeled by the differential dm…

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Q: Derive a differential equation for the orthogonal trajectories of the family  of curves xy=c

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Q: Assume that x and y are both differentiable functions of t and are related by the equation y =…

A: Given :y=cos4xdxdt=-3 when x=π8 Use chain rule to evaluate the dydt. According to chain rule,…

Q: If z = (x + y) ev and x = 5t and y = 1 – t², find the following derivative using the chain rule.…

A: We are given that z=(x+y)ey,  x=5t, and y=1-t2. Now, we need to find dzdt.

Q: Determine the equation of the tangent line to the graph of g(x) = | [1- sin(re')] dt at the /In x…

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Q: Find for the equation below. dy dt

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Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: Use the Chain Rule to find the derivative of w = xy with respect to t along the path x = cos t, y =…

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Q: Find the indicated derivative. dy dt - for y = (2.2t - 4t?)(2t + 1.9) dt 11

A: We have to find dy/dt for Given function.

Q: If z = xy and x = e=' and y = sin(t), find the following derivative using the chain rule. Enter your…

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Q: Find Zxx=Zyy=Zxy=

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Q: Find the number N such that the differential (y^3-2x)dx+Nxy^2dy is exact

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Q: Calculate the derivative a s In (t)dt using Part 2 of the Fundamental Theorem of Calculus. Enclose…

A: ddx∫x8e5x ln(t) dt  Proof:    ddx ∫x8e5x ln(t) =ln (e5x) ddx( e5x ) - ln (x8) ddx( x8)…

Q: Use a linear approximation (or differentials) to estimate the given  number. 28. cos 29°

A: In linear approximation, we estimate the value of the given function or number using the tangent…

Q: Use the appropriate form of the chain rule to find the derivatives. 5.x2 + 5y2 + z²; x psin ф сos 0,…

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Q: Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. d/dx ∫_0^x▒〖e^√t dt〗…

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Q: dw of w: dt x y Use the chain rule to find the derivative 1 with x cos t, y = sin t, z =- dw and…

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Q: Find the derivative of g(x) = |. •r In z Vt2 +t+1 dt

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Q: Calculate the derivative 26 dt d (6£4 dx using Part 2 of the Fundamental Theorem of Calculus. 26 dt…

A: According to the fundamental theorem o calculus:

Q: Calculate the derivative 27 dt d da using Part 2 of the Fundamental Theorem of Calculus. d dx 27 dt…

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Q: 1 - Find a formula for the rate of change dv/dt of the volume of a balloon being inflated such that…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.