(§5.5, Q34) Calculate the derivative d dæ ), Vi dt.

Q: d. (c) dx et 1+t?dt

A: Topic- application of derivatives and integration

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A: We have to find the given definit integral please see the explanation below..

Q: Find the equation of the tangent line at y = 0, given the inverse function x = (3y + 2)(y + 1)? A) x…

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Q: 3. Discuss the natures of the following two equation: ди a?u ди +u at = V dx ax? 1 a²T c? at 1 әт…

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Q: Apply the Fundamental Theorem of Calculus to get the following derivative. d. In( t?+1) dt dx 1

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Q: Apply the Fundamental Theorem of Calculus to get the following derivative. d In (t² + 1) dt dx 1

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Q: Find d2x/dt? as a function of x if d 6x sin x. dt? ||

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Q: Take a look at the derivative of the integral (4t² – 2t + 7) dt. d - dx -4

A: topic - derivative and integration

Q: Evaluate the following derivatives.

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Q: find the indicated derivatives. ds/dt if s = t/2t + 1

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Q: Use Part 1 of the Fundamental Theorem to simplify the following expressions.

A: Let us consider a function ddx∫0xftdt. The fundamental theorem of the calculus states that,…

Q: (a) Evaluate the following derivatives: d ) cos(V5r" - 2)át. s(V5r² – 2)dt . (i) dx J2 d cos V5t – 2…

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Q: Find the equation of the tangent line at y = 0, given the inverse function x = (3y + 2)(y + 1)?. A)…

A: Let's find.

Q: What is the value of f (5) if f (t) sin (Ta) dt :? 1

A: Given, ∫1xfttdt = sinπxx   We have to find the value of f5

Q: · ||r(t)|| dt

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Q: 4- f(t) = ,"t sin(t) e-S'dt

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Q: Evaluate dx f(t) dt and * f(t) dt, where a and b are constants.

A: To evaluate: ddx∫axft dt and ddx∫abft dt, where a and b are constants. Solution: The fundamental…

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

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Q: In Exercises , find the indicated derivatives.9. ds/dt  if s = t/2t + 1          10. dy/dt  if y = t…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: find dy/dx

A: According to Leibnitz  rule of differentiation:

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: calculate the derivative.

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Q: If æ? + y? = 25 and dy/dt = 6, find %3D dæ /dt =

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Q: Write a chain rule formula for the following derivative. du for u = f(v), v = h(s.t) A. du dv at O…

A: Explained below

Q: Use Example 4 to calculate d/dt (r × r), where r(t) = (t,t 2, e t).

A: calculate ddtrxrr where rt=t,t2,et rt=t,t2,et differentiate:-  r't=1,2t,et r x r'=ijktt2et12tet r x…

Q: dy = ay – b dt

A: In this question, we solve the differential equation by reducing into two-part.

Q: Evaluate the integrals

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: In Exercises, find the indicated derivatives.7.  dy/dx if y = 2x3               8. dr/ds if r = s3 -…

A: Given: 7. y=2x38. r=s3-2s2+3 To Find: dydx=?

Q: Evaluate J (sin t + 1)-1 dt

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Q: 크(F(a+) e dt dx 19

A: We have to evaluate, ddxFx4=ddx∫10x4  e-t2 dt

Q: The equation implicitly defines z as a function of t. Find dz dt 11 dt cos (3 z) = -8

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Q: Assuming that y is defined implicitly b equation x2 – y? = 17, the derivative (7, 12) is O 0.58 O 38…

A: We have to choose the correct answer from the given option according to the given condition

Q: If g(x) = | cos' t dt , then determine g'(x). %3D

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Q: Use the Fundamental Theorem of Calculus Part I: d 10. dx J14 n(t + 3)dt

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Q: Given that f has a continuous derivative, compare d d f(t) dt [f (t)] dt. dt to dx

A: Given that, f has a continuous derivative, compare  ddx∫axf(t)dt to ∫axddtf(t)dt

Q: valuate |v(t)dt 1

A: We have given a graph in which the velocity v(t) of an object moving along a line is given where…

Q: Use the Fundamental Theorem of Calculus to calculate the following derivatives: 4 d (a) d.r cos(4t²)…

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Q: Find dv if v = t- dt |

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Q: Compute the derivative: d I/ In(t° + 1) dt dx

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Q: "Differentiate both sides of the equation V = Tr*with respect to t AP (using the chain rule on the…

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Q: Evaluate: L{t f -t e2t Cos t dt}.

A: Evaluate: Lt∫0te2t costtdt First of all we find    L(cost)=ss2+1L(e2tcost) =…

Q: 13. Find the derivative of the function T(z) = dz +b cz +d numbers such that ad – bc + 0. When is…

A: Hello. Since your question has multiple parts, we will solve first question that means question (13)…

Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

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

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

Q: Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. d/dx ∫_0^x▒〖e^√t dt〗…

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Q: Does the fundamental theorem of calculus imply that e' dt = e*?

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Q: Evaluate / (ei + a* ) dt

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Q: g(t) dt = 1. %3D

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Q: Give a physical interpretation of JT. F.ndS.

A: This expression is of surface integral for calculating the area of the field bounded in the…

Q: Using Part I of the Fundamental Theorem of Calculus, 8 d evaluate: dx t7 dt =

A: Given that ddx∫x8t7dt