Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

Q: Calculate the derivative. d sec(8x + 96) dx = sec(8t+96) dt On what interval is the derivative…

A: From the given problem:   ∫67tsec8x+96dx   Applying the Leibnitz rule:…

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 the function. 3 In (x +8) 5-5x O A. dy %3D dx (x + 8)(5 – 5x)? О в. dy 15 -…

A: Given query is to find the derivative of the expression.

Q: Compute the second order derivative f"(x) for f(x) = 3x* -/x. %3D 36x2- 4x2 Ob.36x2 + 3/2 3/2 1 OC.…

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Q: Evaluate the derivative of z f8.png asin (bvx3) f(x): %3D c2x + In(kx) if a = 15.08, b = 5, c = 5,…

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Q: Find the derivative of F(x) = f (t³ - t) ³ dt. O 5 (t³-t) (3t²-1) ○ (x³ - x) 5 ○ 5 (2³-x) 4 O 3t² -…

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Q: dx y=u(1+u°)³ and u =(3x-2)². %3D Express the derivative in terms of x, if

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Q: Find the derivative of h(t) = 15€ + - VE + 6 %3D

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Q: Which among the choices has the first derivative that is e (2x+1) (x +3) ? Of(띠) 3D + 글z2 + 2x-8 O…

A: given function has first derivative is f'x=2x+1x+3    f'x    =2x2+7x+3

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

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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: find the derivative of the function at P0 in the direction of u. ƒ(x, y) = 2x2 + y2, P0(-1, 1), u =…

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Q: 4. Compute the derivative, r'(t), of r(t) = (2t°, v2t, 2 –t=2).

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

Q: (c) Compute the derivative of u = Vt² +2vt³.

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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: Find the derivative of f(w)= sin(4w²)+cos(4w²). A) Swcos(4w°)–8wsin(4w²) B) -8wcos(4w?)+8wsin(4w²)…

A: Given function is  f(w)=sin(4w2)+cos(4w2)Derivative of f with respect to w:f'(w)=…

Q: Take a look at the derivative of the integral * S (6t2 – 5t + 2) dt. (6t² dr Evaluate the…

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Q: Find all second order derivatives for z= 9y e TX. %3D

A: Solution of question as follow

Q: Verify the statement by showing that the derivative of the right side is equal to the integrand on…

A: We will find the derivative of right side. By showing this derivative equal to integrand the…

Q: Find the derivative of the function. rsin(x) In(2 + 9v) dv Jcos(x) y'(x) =

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Q: Find the derivatives of the functions in Exercis

A: The given function is q=2r-r23.

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

A: Solution

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: Find the derivative of F (x) = S (t3 – t)° dt. O 5( – t)* (3t2 – 1) - O (2 - 2) O 5(x³ – 2)* O 3t2 –…

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Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: Fin the second derivative of the fo!lowing functio 1. y = (x²+x+1)? 2. y = x (2x+1)' 3. y = V2a

A: (1) Consider the provided function, y=x2+x+12 Find the second derivative of the above function. Now,…

Q: Calculate the derivative of 2t – 1 > t + 2 r(t) =< 3t – 5, 2t2 + 5t + 7,

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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 second derivative of y = Vx² +x-3 O 6/x O 12/x^5 O 6/x^2 O 12/x^3

A: dxndx =n.xn-1 dcdx =0 ; where, 'c' is an constant number.

Q: With respect to u, what is the derivative of: * 12 בV 2 2 dx Option1 Option3 -'/2 -15

A: Answer is mentioned below -

Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 6x+10y,…

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Q: 4. Show in two ways that the function f(z) = exp(z²2) is entire. What is its derivative? Ans. f'(z)…

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Q: Find the derivative of f(x)= (Inx Oa 6x(Inx Ob. 4 inx Oc 12(in a Od 24(inx

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Q: Evaluate the derivative So (3t² – 2t +1) dt. -

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

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Q: Find the second derivative of vx - Jy= 4 when x = 1. 2 1 -1 -2

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Q: Calculate the derivative by expanding or simplifying the function s(t) = 1 - 2(7t) / (7t)^1/2…

A: Given:s(t)=1-2(7t)7t

Q: Q11) For the z= (2x+3y)10,which is correct ?partial derivative

A: Given,  z = (2x + 3y)10 To find the partial derivatives.

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

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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 derivative ofy. with respect to x if y=(Ix +5) (9x² +2x) %3D

A: Given that: y=(x+5)(9x2+2x)

Q: 3r %3D 5r + 2 – 1 (d) f(x) =

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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: dy Compute the derivative y' dt 2t – 9 - y = 5t 2

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Q: ind the derivative of* T (x) = Va+9x? 63 4s 63 4 3 3 5V5 ) Option 1 Option 4 1 63, 4 63 4 2V 3 Vx 3…

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Q: Find the derivative. dt 12) y = 5t + 6 - 5 1 1 C) 5x + 6 - 5 A) (5x + 6)2 B) 5x + 6 D) (5x + 6)2 36

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

Q: Compute the first, second, and third derivatives of r(t) = 9ti + 5 In(t)j + 5e-3tk. first derivative…

A: As we know that; The Sum/Difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 The Chain rule:…

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: find the directional derivative of f (X, 4) = 3x² + 5y² at the poin t (1,-1) in the dccection of V…

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