2. Compute / f(x)dx for the following function. O if x < 0 3x² if x > 0 f(x)

Q: Зх+1 a) y =- 1 b) g(x)= Vx -

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Q: Find dy/dx of the following function

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Q: d Evaluate the following derivative: dx (1 + t² dt. Oxv1 +x4 + v1+x² Main Content None of these O…

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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: 2- Find O for: y= In (x+5x) dx

A: Tpoic- Differentiation

Q: Compute the second order derivative f"(x) for f(x) = 3x* -/x. %3D 36x2- 4x2 Ob.36x2 + 3/2 3/2 1 OC.…

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Q: ation: tanh’(x² + 3y 3

A: We have to find dydx of following equation. tanh3(x2+3y3)+ex2y4=3        ........(1)

Q: Find the linear approximation of f(x) = lnx at x = 1 and use it to estimate ln(1.02). L(x) =…

A: Given that: f(x)=lnx

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: Q8. Using 1/3 Simpson's rule with h = 0.1 estimate (x - 3x2 + 2). dx

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Q: d Prove In Jax| dx In x for any constant a. dx

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Q: Demonstrate that for the integral of p(x)/q(x) where p(x) is of degree 2 and q(x) of degree 3 it is…

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Q: Drove that 3 e dx converges to 9 3e

A: Explanation and solutions is given below.....

Q: 5. Suppose that f(t) is the rate of snowfall t hours after midnight on December 21, measured in r12…

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

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Q: 4. Differentiate the following function.   y=5e x−5x dy/dx=nothing   Enter your answer in the…

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Q: 17. a. s = ln(4x) Inz I b. 1 IN C. IN d. 1 4x

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Q: Find the following derivative In (x) dx 3 In (x) + 4 In (x) dx 3 In (x) +4 d. 이증

A: Formula

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

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Q: c) h(x) =(5x-1) 12x² – 6 d) m(x) = (4x² – 9x} %3D

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Q: Find the slope of the tangent line to the graph of x²-Iny=0 at x=2 O None of these O 4e4 O e4 O 4

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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: The second derivative for the following function at x = 2 f(x) = V2x + is O 1 O 1/4 O 1/2 3/4

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Q: 2. g'(x) where g(x)=x² +7x-5 %3D

A: In this question we need to find a derivative of the given function.

Q: The derivative of In x is and the derivative of a constant C is, sO X dx = In |x| +C for x> 0.

A: Given x&gt;0, The differentation of natural log x is 1/x  And differentation of constant are zero.

Q: Evaluate the derivative of e22.1.png acos(b/x) f(x) = x2 if a = 73 and b = 0.7 at x = 5 using FDA…

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Q: Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈…

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

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Q: Evaluate the derivative of indicated order of the following functions: d2 (x cos(x² + 3x) а. dx2 d…

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Q: Q1) Find dy /dx for the following function: y = Inln2inx

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Q: Find the following derivative In (x) dx (In (x) +2) d In (x) dx In (x) +2 d

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = er+1) 3- xy +x*y = 3 at x = 1

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Find the following derivative In (x) dx In (x) +2 d In (x) dx In (x) +2 d 이종

A: NOTE: Refresh your page if you can't see any equations. . use the quotient rule for derivatives

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: Compute the derivative d/dx of the following functions: f(x) = x cos^2(4x)

A: The given function is: fx=xcos24x   As we know that; The Product rule: f·g'=f'·g+f·g' The Chain…

Q: Q4. Find the integral of the following functions x dx (x-1)(x2+2x+1)

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Q: Determine for the following function: dy dx y = log3 (x² + 1) ○ (z²+1) In 3 2x O (1²+1) 2x O 2x…

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

A: Solution of the problem as follows

Q: 1. Evaluate the integral: x/x – 1 dx.

A: answer = 1.0667   explanation is given in below step

Q: Find the derivative of the following function. y= In (In (4x)) dy dx

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Q: Find the derivative. y= e at O 4(1/4)x -4(5/4)x In 4 4(3/4)x In 4 4(5/4)x 25 n4 16

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Q: Q4: To evaluate the integral fcos' xdx using the reduction formula of cosinc function

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Q: Derive the following formula for approximating the derivative f": 1 f"(x) ≈ (-f(x+2h) + 16f (x + h)…

A: Given: The formula is f'(x)≈112h -f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h). To prove: The given formula. To…

Q: Given f(x) In(5x) the derivative 5 f'(x) is 1 5x 1 5x O 5 O x5x 1

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Q: Determine the anti-derivative of the following functions: a) S(x)=(3x+2)(2x* - 3x +4)

A: Given, f(x) = (3x +2)(2x2 -3x +4) So  f(x) =  6x3 -9x2 + 12x + 4x2 -6x +8     f(x) =  6x3 -5x2 + 6x…

Q: Find the second derivative of y with respect to x if y = x In(x) - X. А.X In(x) B. In(x) C. In(x)/x…

A: The given function is y=x ln(x)-x

Q: Q1 Evaluate the following: Ine dx n/3 4 sinx 1- Jo 2- Jo x(Inx)2 3-m 2e*cose*dx in 1-4cosx

A: Simple integration problem.....

Q: Find for the following function: dx 4- y = In2 5- tan-1 V4x - 5

A: Topic : differentiation

Q: Find the derivative of the function by the limit process. h(s) = −2√s

A: h(s) = −2√s

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)? dx y logy x

A: