Consider the derivative function 8³ –4/E k (x) = 3 sin æ + What is the general antiderivative of k? Note: Maintain fractions if applicable.

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

A: Find your answer below

Q: 1) Find the derivative of the given function with respects to e 3tan ở In 3 y

A: Given

Q: When f(0)=0 and f(pi)=0, what is the derivative of the function  7e^x + 6sin(x), and what is the…

A: Let the given function be:Applying the derivative with respect to x:Derivative of ex is ex and the…

Q: Find the derivative of the following function. y (In ]x + 4|)7 dy

A: Differentiate w.r.t to x

Q: 1) Find the derivative of the given function with respects to e 3 tan 6 In 3 y

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Q: Find the first derivative of y with respect to x for the following :functions b- y = In( 3x .e-*)

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Q: Find the requested higher-order derivative for the given function. d3y of y = x" - sec(x) dx3

A: Given that y=x11-secx and we have to find third order derivative of y with respect to 'x' that is…

Q: 1) Find the derivative of y = e" tan x

A: As we know that; The chain rule; fgx'=f'gx·g'x And ddxex=exddxtanx=sec2x Given: y=etanx

Q: Find the derivative of the following function. (3x² – 5) y = Cos z + (x² + 1)0* sin 5x

A: Given  y = 3x2-55sin5x + x2+1cosx

Q: Find the first derivative of the following functions with respect to x y = In(ln(In x))

A: To find first derivative of the given function.

Q: Find the derivative of the inverse trig functions. a) y = cos-1 5x b) y = x· arctan x

A: We can solve both the question as below.

Q: Givenf (x) = ln x, what is the derivative function f' (x), and what is its domain? f' (æ) = e², for…

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Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given: f(x)=(sin(2x)+1)7f'π2=?f'(π)=?(a)  f'(x)=?(b)  which is bigger in between f'(π2) and f'(π)

Q: Find the derivative of the function y = In(8 – e-a f'(x) =

A: We have to find derivative

Q: (b) Find a general expression for dy - (x), the (implicit) derivative of y with respect to x, as a…

A: given rθ=2+2cos2θ   for θ∈[0,2π) (b) find a general expression for dydx let  x=rcosθy=rsinθ…

Q: y = (sin x) ³

A: Given function is  y = (sinx)y   this is explicit function of x and y.  So, first we will take…

Q: cos(x) ||

A: If the two functions f(x) and g(x) are differentiable (i.e. the derivative exist) then the quotient…

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

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Q: cos (5x-0.1) w(x) =- e*

A:

Q: Find the 2021st derivative of the following function: y=cos(x) + sin(x) + e* A cos(x) + sin(x) +…

A: Definition used-                         dndxn(cosx)= cos(x+nπ2), dndxn(sinx)= sin(x+nπ2)…

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (x2 ln x)4

A:

Q: Find the derivative of the given function. y = x² sin 'x+x cos 4x

A: For     y=fx gx    dydx=fx ddxgx+gxddxfx   This is the multiplication rule of derivative .

Q: The derivative of In x is and the derivative of a constant C is, sO X dx = In |x| +C for x> 0.

A: Given x>0, The differentation of natural log x is 1/x  And differentation of constant are zero.

Q: What is the Derivative of the following function; y = e-xsinh x

A: Our Aim is to find the derivative of y=e-x sinh(x)-(i)

Q: Evaluate the derivative of indicated order of the following functions: d2 (x cos(x² + 3x) а. dx2 d…

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Q: Find the 25th derivative of g (0) = cos(40 + a) where a is a real valued constant.

A: The given function is: g(θ)=cos(4θ+α)

Q: Let f be the function defined for x > 0, with f (e) = 2 and f', the first derivative of f , given by…

A: Given, f be a function defined for x>0 and the derivative of f is f'x=x2lnx Point e, 2

Q: Find the derivative of y with respect to x. y=log(base)5 e^7x

A:

Q: Find the derivative with respect to x if f(x) = e 2x %3D The derivative with respect to x if f(x) =…

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Q: y = e* arctan x y = arccsc (e*) ICCSC

A:

Q: find the derivative  h(x) = (x + cos^2 x)^8

A:

Q: If y = cos x, then the nth derivative of y with respect to x is equal to itself if n is a natural…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: f(x) = e*

A:

Q: Find the second-order derivative of the following function: f(x) = log2 cos x + ln π

A: We have to solve

Q: 7. y = cos(sin(In(æ))

A:

Q: 3. Calculate the derivative of the following functions. DO NOT SIMPLIFY a. f(x) = tan (In(x) +x² –…

A: Trigonometris identities d/dx(tanx)=sec2x d/dx(in(x))=1/x d/dx(xn)=nxn-1 d/dx(sinh(x))=coshx…

Q: 3. Find the derivative y'(x) implicitly. cos?x + cos²y = cos (2x + 2y)

A:

Q: Compute the derivative d/dx of the following functions: f(x) = x cos^2(4x)

A: The given function is: fx=xcos24x   As we know that; The Product rule: f·g'=f'·g+f·g' The Chain…

Q: find the derivative. y = cos−1(x2)

A:

Q: The third derivative of the function y = e2a with respect to x is

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: ..] Find the derivative of the following functions: a) (e* sin 5x) b) y = csc x +e** csc x+e*

A: Apply the product rule, (f.g)'=f'.g+f.g' Add/sum rule, ddx(f±g)=f'±g' Derivative of sine function,…

Q: (x² +SJ° In 14-X つ. dr

A:

Q: Obtain the derivative of the function f(x) = 6cos(2x) TC and find the value of this derivative when…

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Q: Find the Derivative Function for the following function, y=cos(x)-3x

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Q: 3. Find the derivative of the following function. 8(x) = cos"(vx)

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Q: Find the derivative: 1+e5 f(x) = = COS 1.

A: The given function is f(x)=cos1+e5x1-e8x

Q: Find the derivative with respect to x of h(x) = e2x²+6 In(x).

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Q: f(x) = e²x cos(x) e2

A:

Q: Consider the derivative function g (x) = 3 cos (4x – 1). %3| What is the general antiderivative of…

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Q: 11 with respect to x is The derivative of y = cos - 1

A: