Use this definition to compute the derivative of the function at the given value. h(x) = 5x² + 1 X = 8 %3D h'(8) = Additional Materials

Q: Find the nth derivative of the function y=xex at x=0.

A: To find the nth derivative of function y.

Q: Find the derivative of the function. f(x) = In(sinh(x)) f '(x) =

A: f(x) = ln(sinh(x)) here we use chain rule f'(x) = cosh(x)/sinh(x) f'(x) = cot(h(x))

Q: Find the 4th-order derivative of the function y=xsinhx.

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Q: Can you help me with this problem step by step?

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Q: Find the derivative of function.

A: To find the derivative of the given function                                                y=log…

Q: Find the derivative of the function. y = 3x e -X - 3 ex3 dy dx

A:

Q: Find the derivative of the function. 5x g(x) = [¨ cos(r}]dt cosx

A: We will use Lebnitz rule to differentiate the function .

Q: L(x) = In(x)+log,(x)

A: Used formulas : ddx(logax) = 1x ln a ln x = loge xloge e = ln e = 1ln 5 =1.61

Q: Find the first order derivative with respect to y of the function u = log(x + x² – y2)

A: Using derivatives.

Q: Find the derivative of y with respect to x of y = xlnx – x.

A: Using rules of differentiation.

Q: Eョ2 T -(X子 ノ = (X)J fi(3)

A:

Q: A) Find an equation of the line tangent to the function of x + (y-x)' D9 atx 1. B) Using the…

A: Part A,Given,          The function is x2+y-x2=9 at x=1.

Q: Find the derivative of the function below. F(x) = arctan e a*) f'(x) =

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Q: X+3

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Q: The nth derivative of y = Inx is given by %3D

A:

Q: Find the derivative of the function

A: The derivative of any function y=f(x),containing the variable x is defined as the rate with which…

Q: Find the derivative of the function. %3D y = log |3- 5x| dy

A: Here , we will differentiate y  with respect to X  .

Q: What is the second derivative of f (x) = e²?

A:

Q: What is the derivative of y = e2 +1, with respect to x?

A: Formula used

Q: Z = 1+x2 ; d'z/dx?

A: Given: Z = 21+x2 To find: The derivative, d2 Zdx2 in simplified form.

Q: Find the derivative of the function f(x) = ln(sinh x)

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Q: Which is the second derivative of y=vx ? *

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Q: Why is the derivative of f(x) = e^2, 0? Would e to any power be 0?

A: Given f(x)=e2As the given function is in terms of x and the given function e2 is a constant

Q: Consider the derivative function h (x) = 5x³ + 3x² – 4x + 4. What is the general antiderivative of…

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Q: Find the derivative of z=(ln5)e^x dz/dx=

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Q: find the most general anti derivative  f(x) = e^2

A: A function F(x) is called an antiderivative of f(x) if F’(x) = f(x).   The function f(x) is the…

Q: Solve for the derivative of y = x(e*) %3D

A: Find your answer below

Q: Find the derivative of the function. h(x) = x² arctan(8x) %3D

A: To find the derivative of hx=x2tan-18x

Q: Find the second derivative of the function.

A: Given the function: g(x)=x + ex  ln(x) We have to find the second derivative of the function. Let's…

Q: 3x g(x)=e* In(4x+1) (с)

A:

Q: find the derivative of the function.

A: h(x)=xcosx

Q: Find the derivative of hyperbolic function 1) h(x) = sinh(r2)

A: we have to find derivative

Q: Find the derivative of the function y = 2x − cosh √x

A: The given function is y=2x-cosh x. Obtain the derivative of y=2x-cosh x as follows.

Q: Find the derivative of the function. 10 f(x) = + 6cos x Vx

A: Differentiate above equation with respect to x

Q: Calculate the derivative of the following function. = (x + 8) (x² - 1))° dy dx

A: By using the following equations we can find the derivative of the given function.

Q: Find the derivative of the function. f(x) = e In( Vx + 8 f'(x) =

A: Given, f(x) = ex ln(x+8) We have the formulas d(ex)/dx = ex                       ...........(1)…

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

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Q: The derivative of xª at x = e is equal to .Soloot ono

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Q: Find the given flx), + 2x derivative of function. %3D a+x

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Q: find the 2nd derivative of the function defined implicity by the equation x^1/3+y^1/3=80

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Q: The 60th derivative of x with respect to y of y = x^60 is 60!x

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Q: Find the derivative of the function. h(x) = ∣x∣ cos x

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Q: Find the derivative of the function. f(x) = ln x/(x2 + 1)

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Q: Find the derivative of g(x) = fecost dt.

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Q: What is the second derivative of * f(x) = e²?

A: We have to find second derivative of the function: fx=ex2 We know the formula of derivatives,…

Q: Approximate the derivative of y=x² at x=1 by forming small changes

A: We have to find the derivative of the function y=x2 at x = 1 by forming the small changes.

Q: Find the derivative of the function y = csch−1 (1 − x)

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Q: Find the derivative of the function f(x) = 3 ln(x) + e5ª. df = dx

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

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Q: find the derivative of y with respect to the givenindependent variable.

A: