Find the derivative of y with respect to x. y = sin -1(et) OA. 5e 5t /1- e 10t O B. - 5 e 5t /1- e 10t Oc. 5t e |1- e 10t O D. 5 e 5t /1- e 25t

Q: 1. Find the derivative of the following e)y ln x - x ln y = c

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Q: 2 (y – k) y' = 4a Find the Derivative - d/dy Since 4a is constant with respect to y, the derivative…

A: (1). The given expression is:2y-ky'=4a

Q: 9. The anti-derivative of the function f(x) = e² + cost is (a) e²+ sinx+c (b) e² - tanz+c 10. 0.5(x…

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Q: b) Find the derivatives of the following functions: (i) 3x+4 y = tan x+5 (ii) y = e* -cos3x + x log.…

A: Derivatives

Q: A) find the derivatives for the following: 1) y = In(In(sin¯'(e?r))) – 5-Inx 2) Y=sech-1(log, 93*) +…

A: Chain rule for differentiation: Let y=fghx then dydx=ddxfghx=dfghxdghx×dghxdhx×dhxdx Equation of…

Q: . The derivative of y = xe + e" is D. ex А. хе В. хе + е^ С. exе-1 + е‑

A: Given: y=xe+eπ

Q: Q10. Find the first derivative of the following: a. y= sin(cos5x) b. y= In(2x') y=(-5x' +2)* d.…

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Q: 1. Find the derivative d/dx using implicit differentiation of the following functions. Show your…

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Q: 2. Given x³+ y3 = 6xy dy? a. Use Implicit differentiation to find ? dx b. Find the equation of the…

A: a)

Q: dy of the function da Find the derivative x² In 4y = y sin 4x + e2". Answer:

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Q: Q. No. 5. Find the Derivative of the Given functions a) y = e"in: +2x b) f(x) = a+x

A: I have used the multiplication and division rule for derivative

Q: Find the derivative of y with respect to t at t=2 if a) у %3D х + sinх - cos(1 + x+x?) аnd x = (t/t…

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Q: A. If r = r(t) represents the position function at time t of a certain particle, then what do you…

A: first derivative of position gives- velocity

Q: The derivative of the function y = (3e* – x²)(cos x) is: a) y' = (3e* – 2x) cos x – (3e* – x²) sin x…

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Q: Find the derivative of y with respect to the independent variable. y = 10cos T) -.... A. - 10coS TO…

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Q: Compute the derivative of the given function. g(t) = 2t*e' – 4 sin t cos t g'(1) =

A: on doing differentiation with respect to t we get

Q: Can you help me with this problem step by step?

A: Given that

Q: 1. Find the derivative of the functions, do NOT simplify. a. y = In(8 – 3x) | b. y = ln /2.x + 1 3a2…

A: We have to pick the most challenging formula among differential formulas and solve it.

Q: 4) a) Determine the derivative dx of the following functions y = 3** b) 1-3- 3e² 1² c) y d) y =…

A: We have to find the derivative.

Q: x² d. Find dx (e" -tant)dt. tan(x?) a. 2x(e** - tan(x?)) Ob. 2xex - sec?x O c. O d. It is impossible…

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Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 - 7x3 + 21x2 i) y = (x2 +…

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Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 – 7x³ + 21x² - i) y = (x² +…

A: As per guideline we have to solve first three subparts

Q: 2. In each case, find the derivative d (a) z = x* + y and r(t) = In (t) and y(t) = e24, (b) z = 5xy…

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Q: Find the derivative of y with respect to x. y = sin (e 5t) e 5t e OA. 1- e 10t 5e 5t O B. 1- e 10t 5…

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Q: Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not…

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Q: 1. Find the derivative of the following functions. (find y') a. у %3DIn(cos(20)) b. cos(xy) = x - y…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: -1 The derivative of the function y = sin Va at 1 is equal to 4

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Q: 1. Find the derivative of each given function with respect to x. (i) F(x) = | t dt 1+ t2' (ii) G(x)…

A: FUNDAMENTAL THEOREM CALCULUS If f(x) is continuous over the interval [a,b] and the function F(x) is…

Q: -Ive the derivative dy for the function: x dx = e'sint ; y = ecost %3D

A: Given: x=etsinty=e-tcost We have to find dydx.

Q: /4 Find the derivative of y with respect to t. (a) y = In(3te-1) (b) y = esin t (In t² + 1) (c) y =…

A: Given functions,  (a)  y=ln3te-1 (b)  y=esintlnt2+1 (c)  y=tlog3e(sint)(ln3) The objective is to…

Q: IV. Find the derivative of the given function. 1. u = t³(sin ln t – cos ln t) 2. y = e-2* (1 + e-2x)

A: 1) Given:          u=t3sin ln t-cos ln t   derivating on both sides     dudt=ddtt3sin ln t-cos ln t…

Q: Find the derivatives of the following functions: Inx i) y = sin3x? ii) y = e2*cosx iii) y = 3r+5

A: i)y= sin 3x2y' =ddx sin 3x2y' =cos 3x2  ddx(3x2)y'=cos 3x2 (3)(2x2-1)y'=(6x) cos 3x2

Q: 15. Find the derivative of each of the following functions. TE-2 dt (a) f(x) = /" eV7t-2 %3| (b)…

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Q: IV. Find the derivative of the given function. 1. u = t³(sin In t – cos ln t) 2. y = e-2* (1 + e-2x)

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Q: Vw Find the derivative of y = 3W with respect to w. dy dw

A: To find dy/dw

Q: A. Find the derivative of the function at o P in the direction of A f(x, y) = x V3sec-1(2xy)at P.…

A: To find the derivative of given function means we have to find the directional derivative of the…

Q: 4. Find the indicated higher-order derivative of the given functions. d'y а. у %3D 8е* + sin x; dx7…

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Q: can you help me step by step with this problem?

A: Find the derivative with respect to s.

Q: Can you help me step by step with this problem?

A: To compute the derivative of the function.

Q: Calculate the derivatives of the following functions.(a) y= 4x2 + 4(b) y = sin 3x+ 4 cos 2x(c) y =3x…

A: We have to find derivative of the given function. (a). dydx=d4x2+4dx=8x   b.…

Q: Find the derivative of the given functions. 1. D,(x²cos 2x) 1 1 2. y=x+zsin 2x 3. f(x)= sin?(5x + 4)

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Q: Find dy for the given values of x and Ax. 3 y =x° - 6x +8; x = 1; Ax = - 0.1 - 6x + 8; x = 1; Ax = -…

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Q: 1. Find the derivative (dy/dx) of the following functions: c) cos y + cotx = xy d) (3xy + 7)2 = 6y…

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Q: Find the derivative d/dx using implicit differentiation of the following functions. Show your…

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Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (3x' – 2)' u? a) y=…

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Q: 2. Find the first and second derivatives of the following functions a) y = 6) y = e", c) y = In (sin…

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Q: - 18x Find the derivative of y with respect to x if y = e dy %3D dx

A: We have to find the derivative

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Wr have to find the derivative of the given function first.

Q: Find the derivative of y with respect to the independent variable. 20) y = 7cos TO A) -17COS TO In 7…

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