Evaluate the integsal da a costx t6?Sin'x 2.

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Q: Use integration by parts to find the indefinite integral.

A: To find the indefinite integral I =∫xsec2x dx By using integration by parts, ∫fg'=fg-∫f'gf = x ,…

Q: Evaluate sin (Inx) dx. Int second integration by parts

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Q: Calculate the derivative with respect to x of the other variable appearing in the equation. exy =…

A: Given, exy=siny2

Q: fx sin(5x)dx

A: use integration by parts take

Q: Use implicit differentiation to find y'. 2. e2x = sin(2x + 5y)

A: Solved below

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

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Q: Which order of differentiation will calculate fxy faster: x first or y first?  a. ƒ(x, y) = x sin y…

A: The given function is,

Q: tan (Int) dt

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Q: Evaluate ∫x3 √(1 - x2) dx using integration by parts.

A: Consider the given integral Here the objective is to evaluate given indefinite integral.

Q: use integration by parts to evaluate sinh x cosh xdx

A:

Q: Use implicit differentiation to find dy/dx in x3 + y3 = 18xy

A: Given equation is Differentiating both sides with respect to x, we get

Q: Evaluate the fsinz integrais belovo sin² xcsc 2x dx

A: Evaluate the integral

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: dy Find by Implicit differentiation. dx

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Q: Use the First Derivative Test to find the relative extrema of ƒ(x)=· sin x on (0,27).

A: The given function is- fx=x2-sinx  Differentiating f(x) w.r.t x- f'x=12-cosx Put f'x=0,…

Q: Before integrating, how would you rewrite the integrand of S(x* + 2)² dx?

A: To solve: ∫(x4+2)2dx

Q: Compute the derivative of (arctan(x))^e^x

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Q: x² sin 2x dx

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Q: Explain how to simplify the integrand of dx before x - 1 integrating.

A: we have to simplify the integrand before integrating ∫x+1x-1dx

Q: Use implicit differentiation to find dy/dx in x4 + sin y = x3y2

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Q: Use differentials to approximate the increase in the area of a soap bubble when its volume increases…

A: Let the radius of the soap bubble be a cm, then the volume of the soap bubble is: V=43πr3        And…

Q: Find the slope to the tangent line of the equation y2e2x = 3y+x² at (0,3) Hint: perform implicit…

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Q: dy Use implicit differentiation to find dx 3 sin (xy) = 8x + 5y

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Q: Find the derivative of ,In sin-1) y = e %3D

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Q: Find integration from 0 to π/4  √(secx) tanx dx

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Q: Calculate the derivative of y=arctan√ex at x=0.

A: We differentiate both sides with respect to x using the chain rule.

Q: Find the antiderivative of x/sqrt (x2+1) and verify it by differentiation?

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Q: Evaluate f x³e2x dx using integration by parts

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Q: Evaluate the fellowing de firite integrils (*+) dx (१)

A: using these formula for solving the given integral

Q: Find the derivative of y given that y = In (sinh x) %3D

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Q: Find dy ldx by Tmplicit differentiation. tanLx-y)=

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Q: Integrate SX³1IN x)dx

A: Using integration By parts

Q: Find dy/dx by implicit differentiation for tan-(r²y) = sin(²) + 3xy

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Q: Find the derivative. du a. by evaluating the integral and differentiating the result. b. by…

A: By using Leibniz rule

Q: Evaluate the integral ∫dx / sinhx.

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

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

Q: Explain how to simplify x³ + Vx x3/2 the integrand of integrating. dx before

A: The given integration is ∫x3+xx32dx Solution: To solve the given integration first, separate the…

Q: Evaluate In (ax) dx using integration by parts

A: Follow the procedure given below and use simple intergation by parts.

Q: Use implicit differentiation to find dy/dx in e2x = sin (x + 3y)

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Q: 4х — бу? %3D ху?

A: Find y' by implicit differentiation.

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

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

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Q: 1+y* 3+ sec(y)

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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: dy Use implicit differentiation to find if æ + 4xy+ y² = 2. dx

A: The solution is:

Q: Find the derivative of the function y = tanh−1(sin 2x)

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Q: Calculate using integration by parts: x^3 sin(x^2) dx

A: Given: ∫x3sinx2dx

Q: Find the most general antiderivative. Verify with differentiation f(x)=cosx + 2sec^2x

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Q: Use integration by parts to find the indefinite integral ∫x sec2 x dx

A: Given: ∫x sec2 x dx