10 If f is continuous and f(x) dx = -15, evaluate f(5x) dx. %3D

Q: Show that is C is a function of x with derivative C'=C/x and N=C/x, the d/dx (C/x)=(C'-B)/x

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Q: (Tlog3(cosh z) + csch x) tanh x dx

A: Here we have to integrate the given Integral

Q: dx 3 x + x

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Q: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

A: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

Q: dy for all of: dx Find 3 x(x-2) 2- у %3 x2+1

A: We will use simple differentiation rules to solve this question.

Q: x²y+y°x=-2 .2. X.

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Q: The derivative of y= xh* is O 1) (In x)(xh*-) O 2) 2 an x)(xh*) O 3) (In x)* O 4) xhx

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Q: Find dx * for y = (x² + 2)°(1 – x³)* using logarithmic differentiation.

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Q: Evaluate f S S," x dz dy dx

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Q: Find for the following functions: - dx 1- y = (Inx. Vsin x) 2- f(x) = xcos2x

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Q: Differentiate the function. y=(4x-4)° (3-x)? dy dx

A: Given query is to find the derivative of the expression.

Q: Identify the function, whose derivative is defined below: dy (х + h)2 — х2 lim h→0 dx h А. f(x) — Һ.…

A: Given dydx=limh→0(x+h)2-x2hWe know that the limit derivative formula is f'(x)=limh→0f(x+h)-f(x)h

Q: Evaluate the function: dx (x+1)–Vx+1

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Q: I the second derivative of the function F(t) = 7tsin(º). ver F"(1) =

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Q: Compute f dx, where f(x)=|x|.

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Q: Use implicit differentiation to calculate the value of dy/dx for the given x and y  xy^2 −x^3 =10…

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Q: Find ay for the following functions: dx 1- y = (Inx. Vsin x 2- f(x) = xcos2x

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Q: 2.j -dx 2x2 x-1

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Q: Approximate 2x e 2 dx using three equal subintervals. - 1

A: To Approximate

Q: Find dy /dx for the following function: y = Inln2!nx

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Q: Compute the derivatives: d/dx [ f (x)g (x)]

A: Derivative of function of type uv is given by, duvdx=v.dudx+u.dvdx

Q: dy Find for the following function: dx 1- y = etan'x 2- x³y + x²y = 2 at x = 2 3- y = log4(x³ – x)

A: Finding Derivatives by applying chain rule of derivative

Q: Suppose / (x) = /e*, Evaluate: /f(x) dx

A: Givenf(x)=ex

Q: Find e dx approximately using Simpsons rule with n 10.

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Q: If f(x) is a differentiable function such that f(6) = f'(6) = 2, compute the following derivative. d…

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Q: dy 3- Find dx for the following function: A- y = ecosv3x-1 B- y = x². secx

A: (a) Evaluate dydx of the given function as follows.…

Q: Compute f dx, where f(x)= |x|

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Q: -√x Q3. Change the order of integration and evaluate f* f* dy dx.

A: We can solve as follows

Q: when

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Q: 1+e* dx diverges 0.

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Q: Suppose f(-3) = 3, f'(-3) = 5, = -8, and %3D g(-3) = 1, gʻ (-3) = H(x) = f(x)e®(x). Find the…

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

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Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: find dy/dx for the given value of x.

A: Finding dy/dx

Q: Find dy/dx by implicit differentiation for the following.:y l n x + 2 = x3/2y5/2

A: Consider the equation. y ln x + 2 = x3/2y5/2

Q: Find the second derivative f"(x) for f(r) = e(z+2)*.

A: Given: fx=ex+24 for finding second derivative of given function we first take log and find first…

Q: Evaluate the function: ( e* +1 dx et

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Q: find dy/dx by implicit differentiation for: f(x)=In (2x+1)^3/squareroof of x^2+1

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Q: Evaluate dy for f(x)= (square root of x) +3 where x=9 and dx=0.12

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Q: Find f(2x)dx if f(x)dx = 1. Enter the exact answer. f(2x)dx

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Q: 14. Evaluate y" or d'y of the function when x = 0. dx'

A: To find the y'''for the given equation 13x3+13y3=132  at x=0

Q: Use the Simpson's rule to estimate e**dx with n = 4

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Q: T* dx from a=-1 to b-1 is an even function.

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Q: If f(x) • g(x) is to be integrated with respect to x, taking dx as the differentiated variable,…

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Q: Differentiate the following function. y=3ex−3x dy/dx= ?

A: Solution of the problem as follows

Q: Find dy/dx by implicit differentiation. x6+y7=45

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Q: Show that, for a function f(x) with anti-derivative F(x), d s)ds f(x). %3D dx a

A: Suppose f(x) has an anti-derivate F(x), v(x) and u(x) are differentiable, then Leibniz's rule of…

Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: With n > 0, does x" dx get larger or smaller as n increases? Explain graphically.

A: Given: The given integral is ∫01xndx. Calculation: Use the integral formula, ∫xndx=xn+1n+1+C.…

Q: Differentiate the following function. y= 3 e*(3+5e*)? dy dx

A: According to the product rule of differentiation we have: ddxf(x)·g(x)=f(x)·g'(x)+g(x)·f'(x)