d [sech-(3x)] = dx 3x/1 – 9x²

Q: The first derivative of y = cos(3x-8) is O a. - sin( 3x-8) O b. 3 sin( 3x-8) O. - 3xsin( 3x-8) O d.…

A: Given function is, y=cos3x-8.   It is differentiated as follows: dydx=ddxcos3x-8

Q: sinh³ (x) cosh (x) dx =

A: we have to evaluate the integral ∫sinh3x cosh8xdx use the formulas,…

Q: 3x+4 3. f(x) = x2+3

A:

Q: Integrate sin^2(7x)-cos(x)

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

A: Integral by parts

Q: How to find the derivative of d/dx [(x^2-6)(2x^2+5x)]

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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: Integrate the square root of (1 - sin² x) dx.

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Q: Integrate cos2x/sin^2(2x+8) dx

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Q: Integrate: S tan (æ) sec³(x)dx

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Q: Express in exact form: In(x² + 1)dx

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Q: Find the third derivative of y = (6x - 1). Show your %3D in negative exponent.

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Q: find derivative d/dx ln(3x/(2x+7)^1/2)

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Q: Integrate tan -1 x dx without using integration by parts.

A: We will find the solution in the following step.

Q: 2x2+x dx x+1

A: Integration ∫2x2+xx+1dx

Q: 1. у %3D 4x? — Зх — 2.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: The integ ral csc(0.5) dx is equal to

A: Follow the procedure given below.

Q: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: Verify the formulas by differentiation. ∫ (3x + 5)-2 dx = -(3x + 5)-1/3 + C

A: Given ∫(3x+5)-2dx=-(3x+5)-13+C Verify the formula by differentiation Consider Right hand side value…

Q: find integral sqrt (1 - 4x 2 ) dx

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Q: solve for the intergral of (2sinx)/(1+cos^2x)dx

A: The integral to be evaluated is  ∫2 sinx1+cos2xdx. Here, we can use substitution method to evaluate…

Q: 3x+4 3. f(x) = x2+3 12 x3+6x2+3x 4. f(x) = 3x

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Q: Find the derivative. 5х + 1 In 5x - 1 dx 5x +1 %3D dx 5x -1)

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Q: Find ∫cosh 2x sinh2 2x dx.

A: To find the value of the integral∫cosh2xsinh22xdx

Q: 14. The first derivative of y = arcsin4x is а. -4 b. -4 C. d. V1- 16x? VI- 4x2 V1– 16x? /1– 4x* -

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Q: Find first and 2nd derivative guncic 2 tan2x 3.

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

Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: Find the function that passes through the point (1,2) and whose derivative is dy/dx = (2/x^3) - 4

A: Topic:- application of integration

Q: Solve using a derivative y= 2x tan (3X+1)}" 3. 2.

A: Consider  y=2x3tan3x+12

Q: Evaluate sec' x dx using reduction formulas.

A: The given integral is: I=∫sec7x dx

Q: Use an appropriate substitution to integrate 24xcos(x2-2)dx

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Q: Use integration by parts to solve tan-1(2x) dx.

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Q: Find the derivative 3x (x4+ 1)5 dx d 3x (x4 + 1)5]- dx

A: To find the derivative of [3x·(x4 + 1)5]

Q: find integral  sqrt ( x2 - 9 )dx

A: Given: I=∫x2-9dx we know that ∫x2-a2dx=x2x2-a2-a22lnx+x2-a2+c                                ..1

Q: aluc of 4 alue of dx. 1+(x – 2)? 1

A: See the details solution in below

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

A: ∫-254x3 dx

Q: Find the given derivative. DX 5x -- Dx 5x 1/3 1/3

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Q: Determine the derivative -d/dv y = 2x³ + 5x - 6 y 1 x² 3x 6x³ + x² − 10x − 3 -

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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

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Q: 1. y= ArctanB %3D 3-V9-x2

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Q: Evaluate ( Sech²(In x) dx

A: In this question we will use basic of calculus i.e concept of integration. First we will convert the…

Q: calculate the integral.

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Q: Find the indefinite integral

A: Consider the integral: I=∫sec42x5dx……1

Q: Integrate: S dx sin ³x cos6x

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

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Q: Jcos" (3x) sin (3x)dx in' (3x)dr

A: topic - integration

Q: - S sech-x tanh x dx 1 2 2

A: From the given problem: I=∫sech12x tanh12x dx=∫sechx2 tanhx2 dx....1 As we know that:…

Q: Ssin(3x) sin(7x) dx

A: