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

Q: Compute the derivative of f(t) = (3t2 + sin t, cos3 t + 8t2, 5tan t) relative to t.

A: d(u+v)/dt=  du/dt + dv/dt

Q: Find the derivative of y with respect to t. 10t y3Dcsc dy %3D dt

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

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Q: Evaluate the derivative d 1/x V1+ t6 dt. dr

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Q: In the integration What is the implicit derivative of u? V9-4x² a. du = 2dx b. du = * - 2dx c. du =-…

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Q: Find the derivative with respect to x of the function r4x t² F(x) = e dt.

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Q: d dx 156. dt 1+14 4°

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Q: Evaluate the derivative of the function r(t)=⟨lnt,3t+1,t2⟩ at t=1.

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Q: Use the Power Rule to compute the derivative.

A: To compute the derivative using using power rule: ddtt-3t=4. Solution: Power rule of differentiation…

Q: Use the Product Rule to compute the derivative: d. Find dt (e + 1)(t + 9)) at t = 13

A: Topic :- Derivative

Q: Calculate the derivative. d cos t dt de

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

Q: find the values of the derivatives ds/dt at t=0 if s = 2/(4 - t)

A: Given function is Differentiating with respect to t, we get

Q: By using the definition of the derivative, use a clear diagram to argue that d S(t)dt = f(x). %3D dx…

A: We have to prove that ddx∫axftdt=fx This will be prove by Newton's Leibnitz rule in this rule we…

Q: Use the Product Rule to compute the derivative: 4((t + 1)(t + 9))|t=13 = d dt

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Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2xy - 3y2, P0(5, 5), v =…

A: The given function is ƒ(x, y) = 2xy - 3y2. Note that fx=2y    and  fy=2x-6y. at P0=5,5,  fx=10   and…

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

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Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

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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: Find the particular anti derivative that satisfies the following conditions:  dy/dx = 7x^-2 + 5x^-1…

A: dydx=7x-2+5x-1-5dydx=7x-2+5x-1-5dy =( 7x-2+5x-1-5 ) dx

Q: calculate the derivative.

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Q: Apply the 1t derivative property to : 1) f(t) = e-2tsin5t 2) f(t) = = cost sint 3) f(t) = e²tsin2t…

A: Solution

Q: Find the derivative of the function. -1 y = (3t – 1)(6t – 5) dy dt II

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Q: Find the derivative of this complex function: where z=x+jy (2+jj?

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Q: Use the Product Rule to calculate the derivative.

A: Given: hs=s-12+2s7-s-1 To find the derivative dhdss=4. Solution: Product rule of differentiation…

Q: Use the Product Rule to calculate the derivative.

A: y=t-8t-1et+t2

Q: Find the derivative of the function at Po in the direction of u. f(x, y) = In( 6 x - 3 y), Po(-7, -4…

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Q: Use the Quotient Rule to compute the following: d ( t2 +1 at t = -4 %3D dt \ t2 – 1 The derivative…

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

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Q: Given the function y = x* e* , find dty dx for x = -1. %3D

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Q: Find the derivative of the function.

A: Given function is, F(x)=∫0e2xln(t+1)dt

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: Find the derivative of the following using the three-step rule Зх-1 1. у3D 2x+5 2. y=Va² +x²

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Q: Use the Quotient Rule to calculate the derivative.

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Q: Calculate the derivative d da 34 dt using Part 2 of the Fundamental Theorem of Calculus. 34 d dx…

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Q: Use the Fundamental Theorem of Calculus to find the derivative. Vx-x1-t2 dt d dx

A: The Fundamental Theorem of Calculus says: ddx∫ag(x)f(t) dt=f(g(x))·g'(x)...(1)

Q: In the integration What is the implicit derivative of u? V9-4x* a. du = 2dx b. du = * c. du =– 2dx…

A: Implicit differentiation of integral

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

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Q: Let f(x) = 8x +x – 7. Find the derivative of f by using the formula %3D and check your result by…

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Q: Use the Quotient Rule to compute the following: d/dt(t^2+1/t^2-1) at t=4   The derivative is:

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Q: Find the derivative df/dt. * f (t) = 2' + In (t)

A: Given f(t)= 2t+lnt

Q: Find the derivative of the function f(t), below. f(t) = In(t® + 2) f'(t) = %3D

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Q: Find the derivative of the function at P, in the direction of A. 2 f(x.y) = 4xy- 4y, Po(6,8), A= –…

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Q: Find the directiona derivative of f (x, y) = In(e* – 4y at the point (0, 0) %3D - in the direction…

A: We have to solve

Q: 3) Use the definition to find the derivative of f(t) = +1 t+1 %3D

A: f'(t) = -1/t2

Q: 3r %3D 5r + 2 – 1 (d) f(x) =

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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: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))

Q: ) R(y) = S, t³ sin t dt

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Q: Find the particular anti derivative that Satisfies the following conditions dy 4x +3 ; y(1) = 8 dx…

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