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Q: Let  y=x+e-x be the equation. Analyze the first and second derivatives of this function at x0=0.6.…

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Q: Second derivatives Find d2y/dx2 . x + y2 = 1

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Q: the derivative of f(y)=4sin^9(y

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Q: Find y ′ and y ″ by implicit differentiation. Simplify where possible. x2 + 4y2 = 4

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Q: y=u² +2u u=v² + 2v v = x² + 2x

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Q: Find the simplified form of the derivative of y = 1+csc 3x %3D cot 3x O y = 3 csc 3x csc(3r)-1 O (E)…

A: We have to find the simplified form of the derivative of  y = 1+csc 3xcot 3x.

Q: two rates are related using y=x^2+3. find the derivative when x=1 , given that dx/dt = 2 when x=

A: Given that: y=x2+3

Q: Find the derivative of the function. y = ex5

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Q: II. Obtain the required order of derivative. 1. y? = 4x, find y" 2. x3 - y3 = c³, find y"

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Q: Qol find the derivative of: - f(z) = (2+22²1/2²) ¹/3 14 3) f(²)= (1+2²) ³/2 -3 7 f(z) = (iz-1)³

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Q: State both forms of the Chain Rule for calculating the derivative of y = f(g(x)). State both forms…

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Q: Second derivatives Find d2y/dx2.

A: 2x2+y2=4

Q: f(r, y) = 7xʻy +e sin(y), P= (3,0) Direction of fastest increase is j Direction of fastest decrease…

A: The function is

Q: 4) what is the first and second derivative of the equation W=8z^2 e^z

A: From the given problem:   w=8z2ez   Applying the product rule:   f·g'=f'·g+f.g'   So,…

Q: A challenging derivative Find dy/dx, where

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Q: 18. 2x + y + 4 = 0 is the tangent line to the curve y =x + bx + c at the point (8, - 20). Find the…

A: Here we find the slope of tangent at x=8.

Q: Final Final Answer: 8. Find the 2nd derivative of Answer: 3 y = In(7 – x³) 9. Find the 3rd…

A: In the question we have to find derivatives of given function.

Q: 10. y = -3 cot 2x, 2nd derivative

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Q: ) Find the directions in which fincreases and decreases most rapidly at point P. Then find the…

A: Given: f(x,y)=6x2+8xy+y2,  P=(3,2) To find: (a) Direction of fastest increase (b) Direction of…

Q: 2+ cosh r (r² + 4) Compute the derivative of y = In I - (r+ 1) Compute the derivative of f(x) =…

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Q: Calculate the second and third derivatives. y= 2x^4 −4x^2 +2x

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Q: d²u If u3 = a²t, find dt?

A: Given,             u3=a2t

Q: Find the derivative of the trigonometic function, no chain rule please! 2.2 & 2.3 rules only…

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Q: Second derivatives Find d2y/dx2. 2x2 + y2 = 4

A: To findd2ydx2of 2x2+y2=4

Q: Find the derivative of the function. y · ==—=[x√ 49 − x² + 49 arcsin( - Step 1 Rewrite the given…

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Q: 4) Calculate up to 5th derivative the equation y 2e-4x 5) Calculate up to 3rd derivative the…

A: Given:4. y=2e-4x5. fx=5x2x+47

Q: Find the derivative of f(y) = ee&4) (Y) f' (y) =

A: Given:      f(y) = ee^(y^4)

Q: ind the first derivative of the function: y = 4x - 2x3 + 5 (ii) Differentiate the following…

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Q: Use the product rule to find the derivative of y (3z + 5) (3z - 5). Type your work step by step and…

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Q: Find the derivative of the function. y = x + 5 y' = Your answer cannot be unde

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Q: higher order derivatives x + xy + y = 1 , find y′′

A: The question is about Implicit differentiation. In implicit differentiation, we do not separate the…

Q: Find the derivative of f(z) : (z+2)5 z-i

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Time left 0:39:52 Q The derivative of y= In(5+2x³)* is 4. 5+2x3 6x2 (5+2x³)ª Fim 24x2 5+2x3…

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Q: Find the derivative of the function. y = Vx(x – 9)² y' = Need Help? Read It Master It

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Q: r*y" + 31?y" =1+r

A: Consider the provided D.E,

Q: f(x, y) = 7x²y+ e2=Y sin(y), P= (3,0) Direction of fastest increase is Direction of fastest decrease…

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Q: describes the derivative of a in terms of y. The notation dy O FALSE O TRUE

A: Answer: True.

Q: Find the derivative of ƒ(z)= 5z10 – 23 +2 f' (z) = %3D

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Q: (a) Find the first and second derivatives of the following function (1² + x)(x² – x + 1) f(x) = %3D…

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Q: Use implicit differentiation to help you find the value of the gradient for the equation x^2 - e^y =…

A: Given x2-ey=yx-2+8

Q: A) Differentiate y = 4V +- + 10 B) Find the second derivative of y = 4F +-+ 10 C) Find the…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: Z= 5t^11/5-2t^7/4-t^1/2+7 Fine the derivative

A: Given

Q: Calculate following derivative if y(t) = 5t-3 + 4t². %3D (Use symbolic notation and fractions where…

A: We have to find

Q: I. Find the derivative of y with respect to x. using inrement method x +7 1. у%3х? -3х -5 2. y = Зх…

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Q: higher order derivatives find y'' y = 1/x2 + 2x2

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Q: Compute the derivative of the function y using derivative rules. y = (13x4 +5 - 5)³ (Express numbers…

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Q: find derivative of f(u) = u^6 e^-u

A: Given:fu=u6e-uDifferentiation formula:ddxuv=vu'+uv'

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: