differentiate the following function  f(x)=x2Cos(x)Cot(x)

Q: f(x) = (x + 2)2/3 -

A: First we have to find f'(x) . And to find extrema by first derivative test we have to find all roots…

Q: Find the 28th derivative of the function f(x)= cos(x). The answer is function _____

A: The first derivative of sin(x) is cos(x). And the first derivative of cos(x)=-sin(x). Hence, second…

Q: Compute the derivative f'(x) for f(x) = log(x*) sin(x³).

A: Topic - derivative

Q: Determine the derivative of f(x) = 3 x2 In x with respect to x. f '(x) :

A: We differentiate both sides with respect to x and apply the rule d/dx(uv)=ud/dx(v)+vd/dx(u)

Q: Find the second derivative of the function. f(x) = x cos(x) f"(x) =

A:

Q: Find the derivative of the function. g(x) = arccos(x) / x+7   g'(x)=__________________

A:

Q: Determine the derivative of the following function by applying the quotient rule.…

A: The given function is: h(x)=ln (x2+x)x2+1 The quotient rule for the derivative is given by:…

Q: Find the derivative of the function. f(x) = sin(x) cos(5 – x²) f'(x) =

A:

Q: compute the derivative. f (x) = 9 sec x + 12 cot x

A: We have to compute he derivative of the function: fx=9 sec x+12 cot x We know the formula of…

Q: Find the derivative of the function. f(x) = In(x + 1) f'(x) =

A: To find the derivative of the function fx=lnx+1

Q: Determine the derivative of f(x) = 3 x² In x with respect to x. f'(x) = |

A: We have to find f'(x)

Q: 2 Using the definition of derivative, prove the following: (a) f'(x) = x if f(x) = x %3D

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Q: Find the derivative of f(x) with respect to x ( f(x) = cos(x), find the f(x) by using the…

A: Given;  f(x)=cosx.

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

A:

Q: Find the second derivative of the function.

A: Given: fx=x cosx Now to find the derivative of the given function, Differentiate given function with…

Q: Find the second derivative for the functions defined as follows .p(x) = sin(x2)

A: We have to find second derivative of the function: px=sinx2 We know the formula of differentiation,…

Q: Find the derivative of the algebraic functions: f(x) = x (1 - 4/x+3) g(x) = x + cot x

A: Find the derivative of the algebraic functions: f(x) = x (1 - 4/x+3) g(x) = x + cot x

Q: Find the derivative of f(x) = x° cos x f'(x) =

A: we have to find derivtive

Q: Determine the derivative of f(x) = ( In x )6 with respect to x. f'(x) =

A:

Q: Find the derivative. g(x) = cosh(In(x)) g'(x) = ||

A: To determine the derivative of the function.

Q: Find the derivative using the definition of the derivative for f(x) = Vx (ie. f'(x) = fn &+h)-{(x) ,…

A:

Q: find the derivative. y = ecos−1 x

A: Given: y=ecos-1(x)

Q: 2. Using the definition of derivative, prove the following: 1 (a) f^(x) = if f(x) = Vx 3/x (b)…

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Q: Differentiate the function   f(x) =    1/  ln x

A: Given function is fx=1lnx We know that 1an=a-n So, given function can be written as fx=lnx-1 Before…

Q: Compute the derivative. f (x) = sin x cos x

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Q: Compute the derivative.

A: Given function is Here, we use product rule of differentiation to find f'(x)

Q: f(x) = 2 tan-(x) – 4"

A: Please refer the attached image for complete solution.

Q: Prove, using the definition of derivative, that if f(x) = cos x then f ' (x) = - sin x

A: we have to prove by using the definition of derivative that if f(x)=cosx then f'(x)=-sinx   as we…

Q: Sin X I+ COS f' (x) =>

A:

Q: Find f′(x) from f(x)=2x^3−x^2−x+2 using the definition of a derivative. (Do not include "f′(x)=" in…

A: we have to find f'(x) using limit definition of derivative

Q: Find the derivative. f(x) = 2^x {ln[cot(x)]}^2

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Q: x² sin(x) 8. k(x) = cos( x

A: The given function is kx=x2sinxcosx

Q: Find the derivative. f (x) = e* COS X %3D

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Q: 7. Determine the derivative of the function with respect to x. ソミx

A:

Q: Find the derivative of the function. Simplify where possible.

A: Here given function gx=1-x2 cos-1x

Q: Find the derivative of the following function g(x) = e¯*arctan x

A:

Q: 2. Using the definition of derivative, prove the following: 1 (a) f^(x)= if f(x) = Vx %3D

A: fx=x3

Q: Differentiate the following implicit function with respect to x : xy² - ? = - cos (v?) - cos

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: When given a function f(x), describe (in common language) what the derivative function f'(x) is and…

A: Solution 1:   The derivative of a function f(x) of a variable x is a measure of the rate at which…

Q: Find f (x) of f(x)= by using the definition of the x- derivative.

A: Definition of Derivative is given as

Q: Find the derivative of the trigonometric function: f (x) -3 cos x + x* sin x

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Q: f(x) = (x + 6 sin x) (1 – 5 cos x -

A: To find the derivative of:f(x)=x+6sinx1-5cosx

Q: Find the second derivative of the function. f(x) = cot x

A: We have to find second derivative of the function: fx=cot x We know the formula of differentiation,…

Q: Find the derivative of f(x) = cot^−1(x^2 + 3)

A:

Q: Find the derivative of the function. 10 f(x) = 3 + 4cos x %3D

A: Given that fx=10x3+4cosxTo find its derivative

Q: Find the third derivative [f"(x)] of the given function: f(x) = 8 sin() %3D

A:

Q: Find the derivatives of the following function f(X) from the first principle xsinx

A: derivative of xsinx by first principl is xcosx+sinx. for this question see 2nd step.

Q: 2. Using the definition of derivative, prove the following: 1 (a) f'(x) =E if f(x) = V

A: The given function is  f(x) = x1/3 To find f'(x)

Q: Find the derivative of the following function. g(x)= 1+cos x / x + sin x

A:

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: