1. Differentiate and simplify: 2x f (x) = arcsin :2 +

Q: f(x) = sec¬'(1+ x²)

A:

Q: Find the derivative of the function.

A: To find: The derivative of the function . Formula used: Chain rule of derivative: Derivative of the…

Q: Differentiate y = (x^2– 4)1/2/(x^2) + (1/2)[Arcsec(x/2)].

A:

Q: SOLVE USING VAREATION Of PARAMETERS OR REDUCTION of ORDER 2 tan'x

A:

Q: Integrate the function by using trigonometric substitution. dx, x < 2

A:

Q: show how to use integration byparts to find integration (arcsin x)^2 dx

A: Let I=Arcsin x2 This can also be written as: I=sin-1x2 Now if we want to integrate above function we…

Q: 10. F(x) = Arcsin %3D Vx2 + a?

A:

Q: Find y" by implicit differentiation. бх2 + у2 %3D 3 y" =

A: Given that implicit function is 6x2+y2=3 To find: y''Solution:6x2+y2=3 Diffranciate w.r.t…

Q: Evaulate the intergral: ∫−10sec^2(x)tan(x)dx

A: Consider the given integral:

Q: Evaluate the definite integral.

A:

Q: Find the derivative of the function y = tan(arcsin x)

A:

Q: a) f(x) = (arcsin6x)® b)f(x) = arctan (In x)|

A: Using chain rule of differentiation

Q: Transforming dx using miscellaneous substitution will yield to secx + 1

A:

Q: Differentiate the function.

A:

Q: Differentiate f(x) = arcsin(3x). Use exact values. %3D f'(x) =

A: Solution is written in below steps.

Q: f(x) = Arc tonX 1-x2 Arcsinx %3D

A:

Q: Find dy/dx of inverse tan(1/x) multiplied by secant(x)

A:

Q: 2. Arcsin(x/y) = 4x + 3y

A: Given: sin-1xy=4x+3y We know that ddxsin-1x=11-x2…

Q: 1. y = Arcsin(- x²+4'

A: Given: y=arcsinxx2+4 Differentiate the equation with respect to x.…

Q: Evaluate the definite integral.

A: Given,

Q: Find the derivatives of Inverse trigonometric y = arctan (1+4x) у 3 arcsin (1-2x) у 3 arccos V1 -х

A:

Q: y = cos (arcsin væ) + sin ( arccos 2

A:

Q: Solve the equation for x  arcsin√2x = arccos√x

A: The given equation is sin-12x=cos-1x

Q: Evaluate f sin (2(V1-) dx

A:

Q: Find the point of inflection of the graph of the function f(x)=sin(x/2), [0,4pi] (x,y)= Describe…

A: Derivative f'(x) = 1/2cosx/2 and second derivative f''(x) = -1/4sinx/2; To get inflection point let…

Q: y = arcsin sin (4x²)

A: To find the derivative y=arcsin sin4x2

Q: Compute the derivative of f(x) = arcsin(x? e

A: Given f(x)=sin-1(x2e3x)

Q: How many periods of the function y = tan x are there between -27T and T? %3D [?]

A: We have to find

Q: Use implicit differentiation to find given the relation arctan(5x + y) = 5x2. dx

A: First do some simplification of given relation than use the chain rule of derivative and simplify.

Q: find the largest and smallest value of the function y = 3-sin3x

A:

Q: Find dyldx by implicit differentiation. 9 + x = sin(xy²) dyldx =

A: The objective is to find the derivative by implicit differentiation.

Q: Evaluate sec' x dx using reduction formulas.

A: The given integral is: I=∫sec7x dx

Q: a. arcsin x dx

A: Our Aim is to evaluate the integral given below:-∫01 sin-1 (x) dx -(i)

Q: (y)2 1-y2 1- * when x = 1. Answer: Arcsin x Arcsin y = 3

A:

Q: Find the derivative of the function. y = xV 25- x2 + 25 arcsin 2

A: Follow next step

Q: 20. Find the derivative: a) y=x' arctan x b) f(x) = arcsin(3x)

A: a) here we use product rule and power rule b) here we use basic arcsin(x) formula and chain rule

Q: Question 2: Compute the derivative of y = arcsin(cos(arctan(r))).

A:

Q: arcsin(4x) arccos (x)

A:

Q: Find the derivative of y = (sin z)arcsin z

A: Using logarithms both sides and take differentiate both sides we have

Q: 4х — бу? %3D ху?

A: Find y' by implicit differentiation.

Q: dx V2x – x2 arcsin(x – 1) + c -

A:

Q: • S arcsin(/x) dx

A:

Q: Evaluate the integral.

A: Let the given integral be y - y = ∫sin-1x2dx            ...............(1)Let,x = sinθ…

Q: If f(x) = 3 sin(4æ) arcsin(x), find f' (x).

A:

Q: Find the derivative of y = (sin x)arcsin x %3D

A:

Q: Calculate f'(1), where f(x) = arcsin(x 2)

A: given, fx=arcsin2x now differentiate given function f'x=21-4x2

Q: a Write down the derivative of arcsinx. b Use integration by parts to find | arcsinx d.x.

A: a. Derivative of arcsin(x) is given by ddx(arcsin(x)) = ddx(sin-1(x)) = 11 - x2

Q: If f(x) = 8x* arctan(3x*), find f' (x). f' (æ) =

A: Answer is given below.

Q: What do we call the point at x= of the function f(x) = sinx? 2

A: