'49 If f is continuous and f(x) dx = 18, find | xf(x?) dx.

Q: Find the implicit deriviate (dy/dx) of (2x+3y)1/3=x2

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Q: e*(1-cos(x)) Exercise: Evaluate S dx.

A: Now evaluate the integral, ∫0∞ex(1-cos(x))xdx Take the minus as outside and it is concluded as…

Q: In(x) 1. Evaluate -dx if possible. If not possible, explain why.

A: As we know that the integration by parts:- ∫udv=uv-∫vdu

Q: Find the derivative of y with respect to x. 1 y=x' In (x)---x obra d we do O A. 7x5-x² OB. 8x5-x2…

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Q: x In(x) dx, where x >0

A: Given query is to eveluate the integral.

Q: 2. Show that P(1-x)° dx= x'(1-x) dx. %3D 0/

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Q: Which of the following means "first derivative" * O f(x) O y' O dy/dx all of the above

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Q: dy by implicit differentiation if dx 3 9. = 1. Find - -

A: The given function is 3y+9x=1

Q: 13. We know that x = r cos 0 and y = r sin 0, then find the derivative af/ar if 1 f = ? + y?

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Q: I. Find dy/dx of the following: 1. y= In 2x 2. y (In x) 3. y= In(tan x)

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: A-The derivative is y = ln sin 0 cos 0 1+2ln 0

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Q: dy - år if y = In (sinh 50) and x = cosh 40 dx

A: Solving the problem by doing the derivative.

Q: If; of t = x then at t=1 is (Note that these functions in N) dx

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Q: Compute the derivative d/dx of the following functions: y = 2 sec x − csc x x cos^2(4x)…

A: y = 2 sec x − csc xDifferentiate w.r.t.xdydx=ddx( 2 sec x − csc…

Q: e (sinh x dx + cosh x dy) = 0

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Q: Find the indicated derivative. dp for p q² + 2 5q – 3 %3D dq dp dq II

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Q: Find the derivative of the function. rsin(x) In(2 + 9v) dv Jcos(x) y'(x) =

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Q: Find dy/dx if f(x) = csc (x³ + x + 1)

A: Derivative of the function

Q: 3. S sin x In(cos x) dx

A: According to company rule, we can answer only first question.

Q: fro(x- dt show that = f(x). dx y 3

A: y=12∫0xft x-t2 dt

Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

A:

Q: Find dy/dx for f(x)=(Inx)x^2

A: Given:y=fx=lnxx2We need to find: dydx

Q: S2ta J 2tan x In (cos x) dx=

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Q: Evaluate the function: S de x(x-2) -dx (x–1)³

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Q: Prove that d /dx ( cot -1 x) = - 1/ ( 1+ x 2 )

A: we have to prove that: ddx(cot-1x)=-11+x2

Q: Calculate the derivative e12x d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus.…

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Q: g(x) - (x)/ A.If f(x) = dt, where g(x) = + sin(tº )]dt, find f'(÷). (1

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Q: 35. Does the graph of Sx*sin(1/x), x + 0 f(x) (o. x = 0 have a tangent line at the origin? Give…

A: Given: fx=x2sin1x,x≠00,x=0

Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: If f(x) = – x Find: S",(f(x))² dx That is find S"(: ,(1 - x)?

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Q: I. Find dy/dx of the following: 1. y= In 2x 2. y= (In.x) 3. y = In(tan.x)

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Q: Q3: dy\dx of f(x)= tan x cot x is

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Q: a) In(x+1)³ dx x+1

A: Given, ∫23ln(x+1)3x+1 dx

Q: Find the absolute extrema of the function on the closed interval.                         y = 3 cos…

A: The given function is y=3cos x on 0,2. Compute the critical points on the given interval as follows.…

Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: A-The derivative is y = In sin 0 cos 0 1+2 ln 0

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Q: Find the derivative y = e* In x In x ex E + e* In x O None of these

A: Use product rule:-

Q: prove that if f = sin x the derivative is df = cos x. S dx %3D

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Q: If f(x) = S dt for x 2 1, find f'(2). 1+lnt

A: Simply use the formula for the derivative of an antiderivative.

Q: 4. Use implicit differentiation to find dy/dx. (a) ye" = x" + 1 In x (b) ymz = x"

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Q: 1 dx is finite -1 X Select one: True False

A: True

Q: The derivative of f(x) = ln( is cos x - Select one: O f'(x) = sinx O None of the other options O…

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Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

Q: 13. F(x) = sin t dt 20

A: We need to definite integral properties  also integral of sinx is -cosx

Q: 3. F(x) = " In(x) (4t + et) dt. Find the derivative of F(x).

A: Given, F(x)=∫1ln(x)(4t+et)dt To find : Derivative of F(x) By using the second fundamental theorem of…

Q: 10. Let y = In(x' + sin 3x). Find dy/dx.

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Q: y=sin-1x

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Q: Find the derivative of y with respect to x. y = tan(In 4x) O A. x/1+ ( In 4x)2 1 О в. 1+ ( In 4x)2 4…

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Q: Show that d/dx(ln kx) = d/dx(ln x), where x > 0 and k is a positivereal number

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Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;