Verify by differentiation that a) / t dt : V1+t2 /1+t² + C; _ b) tan(x)dr = – In(cos(x)) +C, –1/2 < x < n/2 - -

Q: 2) Compute the approximate derivatives of In x I+ x2 fCx) at x-2, using three- endpoint formula…

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Q: Determine the equation of the tangent line to the graph of g(x) =| [1- sin(re')] dt at the In z…

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Q: Calculate the derivative d In (t)dt dx 5 using Part 2 of the Fundamental Theorem of Calculus.…

A: Given ddx∫x5e7xlntdt.

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

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

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Q: suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: Given:        x2+2xy=y3

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(2) = / 1 -dt 1+ t…

A: We will find f'(x) as following.

Q: Vz²+1 ev° dy In a

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =…

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Q: Calculate the derivative e10x de L9 In (t)dt using Part 2 of the Fundamental Theorem of Calculus.…

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Q: Calculate the derivative 10z d dz In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Use the Fundamental Theorem of Calculus to find the derivative of Cos t -dt t11 -3 dy dx II

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Q: Use Part 2 of the Fundamental Theorem of Calculus to find th. derivatives. dt sin y dy 1+ y? (b) dx…

A: Consider the integral ∫axfydy, where a is a constant. Note that, ∫axfydy will be a function in x.…

Q: 8) Find the linearization of f(x) = 6 + X+1 tan 4 dt at x = 0. 1.

A: On solving this we will get

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of • sin ( z) h(x) = |.…

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Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: b) Find O Using the chain rule to find de x-1 dy of y= dy of y sin 1-xy ) Using the implicit…

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Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. .......Integrate f over the given interval of x, using…

A: Solution:

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

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Q: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

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Q: Calculate the derivative 12x d dx In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

A: follow next step

Q: Find the derivative of F(x) = 4 n sin(t) dt. %3D dx 3x² cos(x)

A: Integral calculus is one of the two main parts of calculus that is concerned with the study of…

Q: Calculate the derivative re8x d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus.…

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Q: Calculate the derivative d In (t)dt dx Ja4 using Part 2 of the Fundamental Theorem of Calculus.…

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Q: d rcos t sin(x²) dx dt

A: Given,            ddt∫1cos t sinx2 dx

Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: Determine the equation of the tangent line to the graph of g(x) = | [1- sin(re')] dt at the /In x…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 3z F(x) = | cos (t°) dt.…

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Q: Calculate the derivative e8x d In (t)dt dæ using Part 2 of the Fundamental Theorem of Calculus.…

A: Given To apply the fundamental theorem of calculus first simplify these integrals so that this…

Q: Find the slope of the tangent line to the graph of f(x) = x· 2e*cos-1t dt at x = 1 Jln x

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Q: Find the local linear approximation of f(x) = tan¯(x – 4) at xo = 5, where Ax = x – 5. Enter the…

A: Given: fx=tan-1x-4

Q: Calculate the derivative In (t)dt da J3 using Part 2 of the Fundamental Theorem of Calculus. Enclose…

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Q: Calculate the derivative a s In (t)dt using Part 2 of the Fundamental Theorem of Calculus. Enclose…

A: ddx∫x8e5x ln(t) dt  Proof:    ddx ∫x8e5x ln(t) =ln (e5x) ddx( e5x ) - ln (x8) ddx( x8)…

Q: Use the Derivative Rule in Section 3.8, Theorem 3, to derive d 1 sec dx x. 지 V - 1 1지 > 1.

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Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

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Q: 11a d dz In (t)dt

A: To find: ddx∫x4e11xlntdt

Q: Calculate the second-order partial derivative of f(x.v) =sin(x³v?) with respect to x and y, that is,…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 5x F(#) = | cos (t) dt.

A: Fundamental Theorem of Calculus Part I :If g(x) is continuous over an interval [c,d] and the G(x) is…

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of sin (z) h(x) = |.…

A: We differentiate both sides of h(x) with respect to x.

Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: Find the line tangent to f(x) = 3x + cos(8x) at the point wherex-0. %3D Oy-x+1 Oy-x+3 Oy-11x+1…

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Q: Repeat Exercise 60, except with these derivative boundary conditions: y'(0) = 0, y'(π) = 1. In part…

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Q: If f(x) = A B tanx 1+e 1+1² 1+e¹ In (secx) √ 1+tan²x 1+ e tanx sec 3x tanx -dt, then f'(x) equals

A: solution:-f(x)=∫0tanx1+t21+etdtApplying leibniz integral…

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 3x F(z) = | cos (t) dt.…

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Q: Calculate the derivative 25 dt dx using Part 2 of the Fundamental Theorem of Calculus. d dx 25 dt =

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y g(y)…

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Q: Calculate the derivative 27 dt d da using Part 2 of the Fundamental Theorem of Calculus. d dx 27 dt…

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Q: Use implicit differentiation to prove that d/dx [ xn ] = nxn − 1

A: Here we use implict differentiating to prove thatddxxn = nxn-1