y = x arctan 2x - In (1 + 4x2) |

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: i. y= ) In (x+3

A:

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

Q: Find the derivative of the function. y = In(t2) – arctan 3 y' =

A: It is derivative.

Q: Find the nth-order derivative of the function y=arctanx at the point x=0.

A:

Q: Find the derivative of the function y = 2x sinh−1(2x) − √(1 + 4x2)

A:

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 y=cos(2x-x^2)

A: Properties used:

Q: Find the derivative of the function. 1 + x 1 - x y = arctan y' =

A:

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

A:

Q: X+3

A:

Q: Find the derivative of y with respect to x. y = sec -1 (3x2 + 1), X>0

A:

Q: Find the derivative of the function. y3 (4x* - 7x +7)* dy dx (Type an expression using x as the…

A: It is given that y=4x4-7x2+74.

Q: Find the derivative of f(x)=arctan(1/x) and simplify

A:

Q: Find the derivative of the function. x + 6 X-6 y' = y = In

A: I have appended the formula used in the solution part of the question.

Q: Find the derivative with respect to x: y = tan(Vx2 – 1) + csc-(x),x > 1

A:

Q: Find the derivative of the function. y = tan(4x2 + 3)

A: The given function is y=tan4x2 + 3

Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 (x2)

A: Given function is y=cos-1x2. Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: cosx y =-

A:

Q: Find the derivative of the function y = 2x arccos x − 2√(1 − x2 )

A: If the two functions f(x) and g(x) are differentiable (the derivative exist) then the product is…

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

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

Q: Find the derivative of the function. y = 2 tan 5x

A: To find the derivative of: y=2tan5x Solution: y=2tan5x Differentiating both sides w.r.t x we get:…

Q: Find the derivative of the function. y = 3 tan(x - V1 + x 1 + x2 y' = ||

A:

Q: Find the derivative of the function. y = 3 tan-(x - V1+ x?

A:

Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

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

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

Q: The second derivative of the function is y = arctan 2x

A:

Q: Can you help me step by step?

A: Given an equation

Q: Find the derivative of the function defined by the equation x+y=arctan(xy).

A: To find the derivative of the given function.

Q: Find the derivative of the function.

A:

Q: Find the derivative of y with respect to x. -1 y = tan (In(2x))

A:

Q: Find the derivative of the function y = x2 Sin x - 2 Cos x.

A: y=x2sinx-2cosx

Q: Find derivative of y=cos(7x).

A: The given function is

Q: Find the 10th-order derivative of the function y=(x2+4x+1)√ex at the point x=0.

A:

Q: Find the derivative of f (x) = sin (5x) %3D

A: The given function is f(x)=sin3(5x)                     differentiate with respect to x,

Q: Find the derivative of the function y, below. 9x(ln x + In 2) – 8x + v2 %3D

A: first, simplify the function  y=9xlnx+ln2-8x+2 y=9xlnx·2-8x+2 y=9xln2x-8x+2

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

A:

Q: What is the derivative of y = arctan(x² +1)?

A: Find the derivative of the function

Q: Find the derivative of the function.

A:

Q: Find the derivative of the function y= sin(x cosx)

A:

Q: 3. y = sin¬(1+x²)

A:

Q: Find the derivative of the function. y = sin2(x2 + 2) y' = %3D

A:

Q: Find the derivative of the function. y = sin (x + 2)

A:

Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM х 1. y= Arctan- 3-V9-x²

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the derivative of the function. 5/1 x+1 In 22 + arctan x %3D X -1· dy dx

A:

Q: Find the derivative of y with respect to x. 58)y tan (In 2x)

A: Firstly, we use the result that  derivative of inverse of tan of x is 1/1+x^2

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

A:

Q: Find the derivative of the function f(x) = sinh 9x

A:

Q: Find the derivative of the function. y = x sin 1/x

A: Given: y=xsin1x We know that ddxu.v=vdudx+udvdx                                                  ..1