Calculate the derivative 27 dt d da using Part 2 of the Fundamental Theorem of Calculus. d dx 27 dt : 5t4

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A: Domain of definition is where X(t) is defined

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

A: Topic- application of derivatives and integration

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Q: dy Use implicit differentiation (as presented in class) to evaluate at dx the point (3, 2) on the…

A: We have to evaluate dydx at the point 3, 2 on the curve x2+3xy-6y=15. We have to use the implicit…

Q: Which of (a) or (b) is equal to d/dx (x sin t)?

A: We have to evaluate ddxxsint

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

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Q: 20 dv on the interval [0, 20] dt du dt 20

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

A: Given, fx=ddx∫1x3lnt2+1dt To Find: f(x) by applying fundamental theorem of calculus.

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

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Q: Find the derivative of y with respect to t. y = t(In 11t)? dy %3D 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: dy Find the derivatives dx of the following functions csin x Vt2 + 1 dt 2

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Q: Find dy/dx by implicit differentiation. (a) Vry = x- 2y +1 (b) y³e2 + 53y = sec(3x)) (:) (b) x = In…

A: To find the implicit differentiation.  We use the , basic product and chain rule of differentiation.…

Q: Find the derivative d dy dy (3y?) = ay + by +c- dt dt dt

A: Proceed as shown below....

Q: find the differential of each function

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Q: Calculate the derivative. d cos t dt de

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

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: 2x g(x) = |VI+t? dt 1+t2 dt %D

A: To find the derivative

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

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Q: Evaluate the following derivatives.

A: Given, ∫x2exsin3t dt We have to find ∫x2exsin3t dt ∫x2exsin3t dt=∫x2exsin2t sint dt ∫x2exsin3t…

Q: Use the Quotient Rule to compute the following: t2 +1 d at t = 2 dt t2 The derivative is:

A:

Q: Use the Product Rule to compute the derivative: Find d/dt ((t^2+1)(t+9)) at t=5

A: To find  ddt[t2+1t+9]    at t = 5 Using Product Rule of Derivatives

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: d Evaluate In(et – t²)dt. Briefly explain your answer. dx '1

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Q: (c) Use implicit differentiation to compute dy/dx: In(xy) = x°y² + e"

A: We have to find the dydx.

Q: Find the differential of each function. (a) y = etan(nt) %3D dy = te tan (Tt)sec?(rt) 2. secʻ(nt)…

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Q: Find the derivative of the function. s = t In |t| ds dt 11

A: The objective is to find the derivative.

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

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Q: Calculate the derivative: d dx * ST (6t3 – 9t) dt = -

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Q: If F(x)= J. x) = [", "+!dt then F'(x) dt , then F'(x)= /3 sint

A: If Fx=∫π3xt2+1sintdt, then evaluate the value of F'x.

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: Find the differential of each function. (a) y = tan 7t dy = %3D 5 - v2 (b) у%3D 5 + v? %3D

A: we have to find the derivative of the following

Q: dt d Use the Fundemental Theorem of Calculuss to find the derivative dx 1v

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Q: Find the differential of each function. (a) y = tan(3t) dy =

A: We have given  y= tan(√3t)  We have to find the differential equation.

Q: Find the differential of the function. 7 + uvw Da + | Dov•([ Daw dT =

A: Given function is By using quotient rule of differentiation

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

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Q: d a) rcos x Int dt b)을 stn(t2) de dx Jn/4 t

A: Use fundamental theorem of calculus

Q: Find the differential of each function. (a) y = tan(v 5t) dy = 5- v2 (Б) у- 5 + v2 dy =

A: Use the basic concept of derivative and chain rule than simplify.

Q: By referring to implicit differentiation techniques, compute dy at point dx (3, t) for the following…

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Q: Use the Quotient Rule to compute the following: d t2 +1 dt t2 – 1 The derivative is:

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Q: d 2x Le arctan t dt dx

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Q: Compute the derivative for r(t) = (cos(8t))i + (sin°(t))j + (tan(6t))k. %3D dr dt

A: Given

Q: Calculate the derivative. 10 d cos* t dt dx

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Q: dx(t) If the PSD of X(t) is Sry(0). Find the PSD of - dt

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Q: Find the differential of the function. Z = e-8x cos(5xt) dz z = dx + dt %3D

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

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Q: Find the differential of each function. (a) y = tan 3t dy =

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Q: Find the differential of each f (a) y = 1 + 4s dy =

A: (a) The given function is: y=s1+4s. The quotient rule of differentiation states that d…

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

A: Given that ddx∫x8t7dt