d -[x*] = xx"-1 dx

Q: Find the indefinite integral sec* 7x dx.

A: To find the indefinite integral of ∫sec47xdx

Q: Find d2y/dx2 by implicit differentiation x3 + y3 = 1

A:

Q: Can you help me with this problem step by step?

A: The logarithmic expression

Q: Use implicit differentiation to find dy/dx in x3 - xy + y3 = 1

A: We differentiate both sides with respect to x

Q: Find tan-1 x2 -dx using integration by parts.

A: Integral by parts

Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

Q: 70ot(*) e*dx e2x +1

A:

Q: Find dy/dx by implicit differentiation. tan-1(4x2y)= x + 2xy2

A:

Q: Express (3*) dx as the limit of a sum. 1

A:

Q: ind the second derivative in its simplified form 1. y= Arctan x / 3- (square root of 9-x^2)

A: 1. y=tan-1x3-9-x2 Differentiate with respect to x…

Q: dx

A:

Q: Find the derivative of the function. y= -6x In (5x + 8) dy dx

A:

Q: dy Find by implicit differentiation dx хЗу — ху3 — а3Ьз

A: Given:- x3 y -xy3 =a3 b3  To find:- dydx of given implicit function

Q: Use differential to approximate the change in y=x3+x2 as x changes from 1 to 0,95.

A:

Q: FIND ANTI DERIVATIVE a) S 2. +9 dx x マ d x 1-4x6

A:

Q: Use the Power Rule to compute the derivative: d. X. dx x=-1

A:

Q: Use implicit differentiation to prove that la"] = d nxn-1 dx

A: ddx(xn)=nxn-1

Q: Use implicit differentiation to find dy/dx. In xy-y = 3

A:

Q: 2x2+x dx x+1

A: Integration ∫2x2+xx+1dx

Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

Q: Solve: The integral of (sec(x))^3 dx.

A:

Q: Find the derivative. d [3x (x + 1)5] dx d dx [3x(x + 1) ³1-0

A:

Q: Find dy/dx by implicit differentiation. tan−1(4x2y) = x + 5xy2

A: Given,

Q: Use implicit differentiation and solve for dy/dx if 6x+(x^3)y+3y^2=10.

A: The technique of implicit differentiation allows us to find the derivative of y with respect to x…

Q: use the Power Rule to compute the derivative.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Use implicit differentiation to find dy/dx in x2(x - y)2 = x2 - y2

A:

Q: Find the indefinite integral.

A: Use the substitution method and consider x2 as u. Differentiate both sides of u=x2 and substitute x2…

Q: roo sin(2) Compute (4) dx. fo x(x²+4)

A:

Q: Integrate x sqrt of (x+4) dx using algebraic substitution

A:

Q: d Use implicit differentiation to prove that x"| = nx"-1 dx

A: Implicit differentiation is a method to solve the differentiation of an equation without the need to…

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Use the rule for reciprocals (수) - - to find the derivative: d 1 %3D dx lx2 Зх + 2

A: Given the rule of reciprocals as 1f'=-f'f2. It is required to find the derivative of 1x2-3x+2. Note…

Q: Find the value of the definite integral: 4x dx -2

A: ∫-254x3 dx

Q: Evaluate integral x^2e^-x^3 dx

A:

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: 1 point) Calculate the integral: 1 dx = (x + 8)(x + 4)

A:

Q: dy Find by implicit differentiation. dx ху — ху" %3 8 -

A: Implicit differentiation: Differentiate both sides of an equation with two variables by considering…

Q: Find the second derivative y=lnx + 3 sin(4x) d²y dx² of

A:

Q: integrate x^4cotx^5 dx from 0.4 to 0.8

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Q: -2(х-1 — х?) dx

A:

Q: Find the indefinite integral ∫sec 4x dx

A: the given indefinite integral is: ∫sec4x dx we have to find the value of the given indefinite…

Q: cosh(In x) dx

A:

Q: ind the second derivative in its simplified form 2. y= 4 Arccos x/2 +2 square root of 4-x^2

A: Given, y=4arccosx2+24-x2

Q: dy Use implicit differentiation to find dx '+x² - y² = 10

A: Given; e^(xy)+x^2-y^2=10 We have to find dy/dx

Q: In (sinh x ), + tanh x j + 1-x k )dx 1- sinx

A:

Q: Find the derivative. d 3x +1 In xp Зх- 1 Зх + In dx 3x-

A:

Q: Without integrating, explain why

A: when the integration is in the form  ∫-aaf(-x)=∫-aa-f(x) is odd then it is equal to 0

Q: Find f tan-1 x dx by using integration by parts

A: We have to find out

Q: Use implicit differentiation to find dy/dx in y2 = x - 1/x + 1

A: