a derivative computation using the FTC and the chain rule t): df 13

Q: With respect to x, what is the derivative of: * du In(u) O Option 2 Option 4 du Option1 Option3

A: apply chain rule

Q: Find the derivative of t(z)= (Z-2)5

A: fz=z-25z2+iz+12 Now find the derivative of fz f'z=ddzz-25z2+iz+12…

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: y=57x3+1-3

Q: Compute the following derivatives using the chain rule. g(y) = ln(1 + y).

A: Take 1+y = t  And use chain rule

Q: compute the derivative. c(t) = 1-li – e2'k - e2

A: Given  ct=1ti^-e2tk^

Q: Compute the derivative of the given function. g(t) = 2t - In(2 – 5t) %3D

A: Given that: g(t)=23t.ln(2-5t)

Q: Differentiate. f(x) = In ( In (8x)) f'(x) = Compute the following derivative using the method of…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 11) y = In 1-x (x +4)3

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Q: Use the Power Rule to compute the derivative.

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Q: Find the derivatives of the functions in Exercise

A: Given: r=21θ+θ We know that ddxxn=nxn-1                                                        ..1

Q: write the function as a composite f (g(x)) and compute the derivative using the Chain Rule. y = (x +…

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

Q: Find the indicated derivative. dp for p q² + 2 5q – 3 %3D dq dp dq II

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Q: Use the Fundamental Theorem of Calculus to find the derivative of y- " cos t dt t12

A: Given that  y=∫-9xcos tt12dt

Q: use the Power Rule to compute the derivative.

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

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Q: write the function as a composite f (g(x)) and compute the derivative using the Chain Rule. y =…

A: Given : The function is y = cos ( x3 ) .

Q: Use derivatives to find two positive numbers a and b such that a^2 + b^2 = 1 and such that 2*a+3*b…

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Q: Find the derivatives of the functions in Exercis

A: The given function is q=2r-r23.

Q: Compute the derivative of g(x) = cos(t) dt-

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Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative.

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Q: Use the Power Rule to compute the derivative.

A: The power rule of derivative is given by dxndx=nxn-1 Using the above rule: dt-2/5dt=-25t-25-1…

Q: to

A: We have to find the derivative according to the given information

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(2) = ], 14F° 1 dt 1+t3

A: Given f(x) = ∫2x11+t3dt First fundamental theorem: if  F(x) is continuous on [a,b] and f(x) is…

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

A: First, we split the integral function into two terms. Now find the derivative of both integrals by…

Q: Find the indicated derivative.dp/dqfor p =q2 + 2/4q-2

A: Given a function in p in terms of q as shown below. We need to compute dp/dq.Here we use (u/v) rule…

Q: f(x) = 2x² cos(r®)

A: Given Data: Function: f(x) = 2x2 cos(x5)   The product rule of differentiation is,

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 67) y = In 8x2

A: Since the expression contains x, we have to find derivative with respect to x.

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

A: To find the derivative of the h(x) using fundamental theorem of calculus part 1.

Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx

Q: find the derivative using the definition ƒ(t) = 1/2t + 1

A: Given:ft=12t+1Derivative definition:f'x=limh→0fx+h-fxh

Q: d rcos t sin(x²) dx dt

A: Given,            ddt∫1cos t sinx2 dx

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(x) =…

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Q: Use the appropriate Product Rule to evaluate the derivative, whe ri(t) = (9t, –1, -t®),r2(t) = (3,…

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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: Find the derivative using the definition fex)- = C fcx) fCx) = そり f ex) = KX" f cx) fx) = gx).hcx) 9…

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Q: Compute the derivative of g(æ) = e dt. 22 -2xe -2xe O -2re

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Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

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

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

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: Use derivatives to find two positive numbers a and b such that a^(2)+b^(2)=1 and such that 2a+3b is…

A: Solved below

Q: Find the implicit derivative given a³ – 2b² = 7ey

A: For the implicit differentiation, we take y as a function of x and a, b are constants. We are given,…

Q: 5. Compute the derivative, r'(t), of r(t) = (et-4, t, In(1 – t)).

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Q: calculate the required derivative using the chain rule. z.ton"() -1 - tan u =Y Cose » yarsin@ az -?…

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Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: Use the u-substitution to find the anti-derivative of h'(x)= xcos(2-3x2)

A: h'(x)=xcos(2-3x2) Formula ∫cos (x) dx= sin (x)+C

Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

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Q: The derivative of Q with respect to r for: Q=In (r+1)' is: 2)

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Q: The derivative of a^u with respect to x is

A: Aim:- To calculate : ddx(au)