What is f'(x) at x = -1 of the function f(x)=x^-2 + (x^2)^(1/2) *

Q: dy Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y³. dx

A: Given that: 3x2 +2xy = -4y3. Find dy/dx. We know that derivative of xn is nxn-1.   Here i attached…

Q: In y = 22 cosh1 2x

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Q: Find the derivative: y = ln² (3x + 1) O y' = O O O y' = y' = y = 2 ln(3x + 1) (3x + 1) 6 (3x + 1) 3…

A: Consider the function y=ln2(3x+1). The objective is to find the derivative of the function.

Q: Find the Equation of tangent line of the function f(x)=1+csc(x)-√cos(x) at the point…

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Q: Find the derivative of the given function. Infsech(x) + tanh(x)) 1) sechx+tanhr sinhx+1 sechx-tanhx…

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Q: 3.

A: Indefinite Integration

Q: Find the derivative. 2 - - dy dx - if y(x) = 1 x + 3 dy dx ||

A: This question is based on Chain rule diffrentiation. d/dx{f(x).g(x)} = g(x)d/dx{f(x)} +…

Q: Find the derivative of the function by the limit process. f(x) = 6/x

A: Given fx=6xddxfx=limh→0fx+h-fxh

Q: 3. Why first derivative is zero at local maximum and local minimum of function in an open interval?

A: Given, Why the first derivative is zero at the local maximum and a local minimum of function in an…

Q: ) y = In³ )) (tanh²(scc '(x²)

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Q: Use forward, backward and central difference to estimate the first derivative of f (x) = In at x =…

A: Given function is fx=lnx and x=3 Step size h=0.01 We have to estimate the first derivative of fx=lnx…

Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

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Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

Q: Compute the derivative of y = ln ( – V1 – 2 cosh x (x° + 2) |

A: To compute the derivative of,  y=ln1-2 cosh x .x3+2x.x-1.

Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: Find the derivative of the function f(x) = tanh(4x2 + 3x)

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Q: Find the derivative of the function. 2x F(x) = arctan(t) dt 1 2 arctan(2x) F'(x) = (arctan(Vx)) -

A: Here we have,

Q: 2.) Investigate the derivate of the function ƒ(2)=Imz by using definiton of derivative.

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Q: derivative of y = arctan(x2+ 3)

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Q: y=9 arctan (x+sqrt(1+x^2) )

A: ddx(xn)=nxn-1 ddxx =12x ddxtan-1(x)=1x2+1 Chain Rule: if f=f(u) where u is a function of x then…

Q: tion of the tangent line to f(x) = 4 %3D

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Q: 2. In y = 2" + x cosh 2x

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Q: Estimate the derivative of f(x) = sin x at x = π/6.

A: Given,       f(x) = sin x at x=π6

Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: What are the formulas for differentiation and intergration? When to use them?

A: Query- What are the formulas for differentiation and intergration and describe When to use them?…

Q: Find the derivative of the function f(x) = arctan ex

A: According to the question, we have to find the derivative of the function fx=arctan ex. The…

Q: Find y''' (3rd derivative) of y = sin^2 (tan(6e^x))

A: Here,              We have given a function and we have to find its 3rd derivative.         So , the…

Q: What is the connection of the concept of limits to slope to derivatives (delta method to simple…

A: The limits of the function at a point are calculated using the formula . The limits are used to…

Q: Find the derivative of the function f(x) = cosh(8x + 1)

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Q: Find a function that has x^6 as its derivative without using integral knowlegde.

A: In this question, we need to find a function that has x6 as its derivative.

Q: Calculate the derivative of y=arctan√ex at x=0.

A: We differentiate both sides with respect to x using the chain rule.

Q: Compute Anti-Derivative (-1 --> 1)  (x^3 + x) / (cos(x) + pi) dx

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Q: Find a function with the given derivative whose graph passes through point P f'(x)= 2xx+1-cosx,…

A: To determine the antiderivative satisfying the given initial condition

Q: Find 1st and 2nd derivative of:   f(x)=(5x^4 + 3x^2)*ln(x^2)

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Q: 15. What is the derivative of the function: F(x) = x cos(5x) F(x) = x cos(5x) F'(x) = (x)…

A: Solving

Q: Explain why a positive derivative on an interval impliesthat the function is increasing on the…

A: On an open interval Suppose  is a function on an open interval  that may be infinite in one or both…

Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: what is the derivative of f(x)=ln(tanhx)

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Q: What is the derivative of f(x)=2sin(x) at the point x=−π/2?

A: To find the derivative of fx=2 sinx, at the point x=-π2.

Q: What is the second derivative of ecON (), , Cosh (A sinh?(x)e cosh (x) + cosh2(x)ecosh («) B sinh…

A: Let the given function is y=ecosh(x).

Q: The first derivative of the function y = 3x cannot be solved using implicit differentiation. Select…

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Q: Find the derivative of the function y = x tanh−1 x + ln√(1 − x2)

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Q: Determine the second derivative of f(x) = x²e²x at x = -2 with a step-size of h=0.50 using Central…

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Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…

Q: Differentiate the functions showing the general process in determining the derivatives. Using the…

A: We need to differentiate given function.

Q: What is the derivative of: 4 ln(sec y + tan y) − 2x − sin 2x = 1

A: Given: 4 lnsec y+tan y-2x-sin 2x=1 To Find: dydx=?

Q: What is the 2nd derivative of y=cosh(x+y)?

A: