Find the derivative of the function using the definition of derivative. 1 g(x) 8 + Vx g'(x) =

Q: find the derivative of the function  f(x) = e5x sec x

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Q: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

Q: (1) Using the definition of derivative, find the derivative of th following functions: (a) y = xvx²…

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Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

Q: Find the derivative of the given function at a given number. 1. y = 3x² - 2 at f'(1)

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Q: 2x+1 Ise Derivative Rules to find the derivative of g(x) x2-1

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Q: (1) Using the definition of derivative, find the derivative of the following functions: (a) y = xVx2…

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Q: Find the 3rd derivative of the function y=excosx.

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Q: 3. Find derivative of the function y = x tan-(4x)

A: we have to find the derivative of y

Q: Find the derivative of the function. y = In(x8)

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Q: Find the derivative of the function. f(x) = ln   x + 2 x − 2

A: Given,            fx=lnx+2x-2

Q: Find the derivative of the function. h(x) = x2 arctan(5x)

A: Given function: hx=x2tan-15x Differentiate the above function w.r.t "X" h'x=ddxx2tan-15x

Q: 14. f(x) = 2 +3cos x

A: using basic properties and application of derivation we will solve this question.

Q: 6. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: By using differentiation. and definition of tangent at point.

Q: y = x*(1 – In x4)

A:

Q: 2. Find the derivative of g(x) = 2x sin x.

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Q: Find the derivative of the function. h(x) = x² arctan(5x) h'(x) =

A: h(x)=x2tan-1(x)

Q: 10)Find the first derivative or f’(x) of the following functions using long method derivatives

A: We need to find derivative of given function.

Q: Find the derivative of the function. 1- e3x 1 + e3x y = cos y' =

A: Given that: y = cos1-e3x1+e3x To find: We have to find the derivative of the given function.

Q: Find derivative of f(x) = ln(5x + 2) The slope (as fraction) of the tangent line at x=2 is

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Q: Find the derivative of the function. 10 f(x) = 3 + 2cos x

A: Recall: dxndx=n xn-1 d(cos ax)dx= a(- sin ax) dc1f(x)±c2 g(x) dx= c1d[f(x)]dx± c2d[g(x)]dx

Q: 5-x. Calculate the derivative of y with re

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Q: y=x²

A: I have stated the used formula in the solution

Q: Calculate the derivative of the function. Then find the value of the derivative as specified. g(x) =…

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Q: Find the derivative of y with respect to x. y = csc-1(x5 + 1) ; x > 0

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Q: Find the derivative of the function. f(x) = ln(x2 + 1)2

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

A: Differentiate above equation with respect to x

Q: Find the derivative of the function. g(x) = 9 + In(x)

A: We have to find the derivative of : g(x)=ex29+ln(x)

Q: Calculate the derivative of the function. Then find the value of the derivative as specified. g(x) =…

A:

Q: Determine the 8th derivative of y with respect to x of the function : f(x) = 1 / 1 + x2 and find the…

A:

Q: 3. Find the second derivative using implicit differentiation x² + y? = 4

A: Given that x2+y2=4To find implicit differentiation

Q: Find the derivative of -3x f(x) = e¯* + e2x - e %3D

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Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: Find the derivative of the function. g(x) = 2(3- Ex)

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Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

Q: 14. Find the derivative of the function using the definition of derivative. f (x) = V1 – x

A: Derivatives

Q: Find the derivative of the function using implicit differentiation.  1.) x³-3x²y+2xy²=12 2.) x²-y²…

A: This question is related to implicit differentiation, We will solve it using given information.

Q: Find the derivative of the function 3- y = e- sin 3x 4- y csc- (x2 + 1)

A:

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A: Applying natural logarithm on both sides, we get

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

A:

Q: Find the derivative of y with respect to x Y=(7x+3)^x

A: Find the derivative of y with respect to x Y=(7x+3)^x

Q: Find the second derivative of g(x) = secx.

A: Given : gx = sec2x

Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x

Q: Find the derivative of y with respect to x. Y=(x^2 ln x)^4

A:

Q: Find the derivative of f(x) = 3/x ln(x), f' (æ) =

A: Chufu