Compute the derivative of the function f(r) = cos(x) by the difference quotient definition.

Q: Find the derivative of the function.

A: Given: To find: Derivative

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

A: Given that,             f(x) = lnx3 Differentiating with respect to x, we get                  f'(x)…

Q: Find the derivative of the function.

A: To Find the derivative of the function. y = ln sec x + tan x

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: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

Q: Find the derivative of the function f (x) = sin°(x) (),

A:

Q: f(x) = cos (x – a -2).

A:

Q: Evaluate the derivative at x = 1 for y = In ()

A: For a function f its derivative is defined as f'(x)=limh→0f(x+h)-f(x)h. For some standard functions…

Q: Find fifth order derivative of the function f(x) = x*Sin (2x +1) by using Leibnitz theorem.

A:

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 f(x) = 2(x² + 3x) cos(sin(x³)).

A: I have used product re and derived of composition of two function

Q: Compute the derivative of f(x) = sin2x

A:

Q: What is the derivative of f(x) = - 3 with respect to r? %3D

A: Given: The function f(x)=-3x3

Q: Calculate the derivative.

A:

Q: Find the derivative of function.

A:

Q: Find the derivative of the function. f(x) = sin-(4x) f'(x) = %3D

A: The given function is: f(x)=sin-1(4x) To find f'(x) here.

Q: Find the derivative of the function f. f(x) = e¯X tan(4x) %3D f'(x) = %3D

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Q: Find the derivative of the function using the definition of derivative. f(x) = rx + q

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Q: Find the derivative of f(x) = (sin a)" %3D

A:

Q: Find the derivative of the function.

A: Given: y=lncosxcosx-1

Q: Find the derivative of the function. 3x2 g(x) • dt 4 + t3 tan x g'(x) =

A:

Q: Find the derivative of cos (x/y)

A:

Q: Find the derivative of f(x) = -1 csc (cos r)

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Q: Compute the derivative with respect to x using differentiation rules.  f(x) = eax cos(bx) for…

A:

Q: Find the derivative of the function. • 2x2 g(x) = 1 dt 3 + t3 /tan x g'(x) =

A:

Q: find the derivative of the function.

A: h(x)=xcosx

Q: Find the derivative of the function by using the chain rule. sinx (a) h(x) = tan(x³ sinx) (b) y= %3D…

A: To find the derivative of the given function using the chain rule, which is:…

Q: Compute the derivative using derivative rules. y = cos(te- 2t)

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Q: Find the derivative of r = In (cos" x).

A:

Q: Find the derivative of f(x) = sin x²+ cos x

A: fx=sinx2+cosx

Q: What is the derivative of f(x)=−cos(x)+4sin(x) at the point x=−π/2?

A: We will find the derivative as following.

Q: Find the derivative of f (y) In(y)

A:

Q: Compute the derivative of f (x) = (x – 3r) cos(r). -

A: You will find the derivative of the given function using the product rule of differentiation which…

Q: Find the derivative of Vry = -3+x*y° using implicit differentiation.

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Q: Find the derivative of f(x) = v3x + 1 using the general formula for differentiation.

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Q: Use the chain rule and product rule to find the derivative of f (x) = e" (sin(x)² + x).

A: Given Data: Function: ex(sin(x)2+x)   The chain rule of the derivative is, ddxfgx=fgxg'x ......1…

Q: (a) h(x) = tan(r'sinx

A:

Q: Find the derivative of the function f(x) v4-x by definition

A:

Q: Find the derivative of the function. f(x) 4. + 2cos x %3D

A:

Q: Find the derivative of f(x) = x cos x using the product rule.

A: The given function is fx=xcosx.

Q: 5. f(x)%3D + cos X

A:

Q: Compute the derivative of the function f (x) = tan x2 +1

A:

Q: Find the derivative of the function. f(x) = In(sinh(x)) %3D f '(x) = %3D

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Q: y = cos /sin ( tan tx

A:

Q: f(x) = cos vx

A: The derivative is defined as f'(x)=limh→0f(x+h)-f(x)h.

Q: Find the second derivative of the function. f(x) = x x sin(x) %3D f "(x) - !!

A: Given:   fx=x sinx  To find: f"x=?

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

A:

Q: sinx (a) h(x) = tan(x² sin.x) (b) y= V1+cos.x

A:

Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

Q: Find the derivative of  f(x) = tan(cos(x^2))

A: f'(x) = d (tan(cos x2)dx  f'(x) = sec2(cos(x2))d cos x2dx               because   d (tan(x))dx =…