dy Given y = 12ln2x- tan4x, its derivative is: Select one: A. 쯔 -4cos 4x В. 12 - 4sec24x c. 2. - D. 은 + 4sin24x

Q: Use the fact that e4x = (ex)4 to find d/dx(e4x). Simplify the derivative as much as possible.

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Q: dy Q5) If y = (tan60)/20 + 1 find dx

A: To find Derivative of the given y

Q: d²y Find dx² x = ² + 2, y = ² + 7t dy dx d²y dx² For which values of t is the curve concave upward?…

A: We have to solve given Questions.

Q: d²y 2. Find the second derivative, dx² a. x = t² + 1 and y = t³ b. x = - t2 + 2 and y = sin(t+ 1)

A: Let's find.

Q: (f) / sec“ y dy. tan5

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Q: Use the alternative fom of the derivative to find the derivative ot Xo C, if it Exits. f(x) = Ix-6l,…

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Q: If f(x,y) = x3y + exy^2, find the derivatives of df/dx and d2f/dxdy.

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Q: dy 12 Given that dx y = 5 when x = 3. Express y in terms of x. %D V5x+1

A: dydx=125x+1dy=125x+1dxIntegrate both sides

Q: dy Q1. By using the "definition of the derivative" find 2 of y = v2x? %3D dx

A: Our Aim is to find the derivative of y=2x -(i)

Q: Calculate the derivative indicated. d²y = where y = + 572 dz? \r=8 Answer:

A: See the detailed information below.

Q: dy the second order derivative dz² For the function y = 14 e O 14e" + 14x O 14e? – 14x O 196e – 14x…

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Q: dy 14. Find the derivative, - dx xVx2 +1 y = (x + 1)²/3

A:

Q: Find the derivative of the function. y = V 3 + 2e7 II y' = %D

A: To find detivative of y=√(3+2e^(7x))

Q: Find the first derivative. y=T° + 2T5 -6T - T-7 P. ( +27 -6T-T-7) = dT

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

Q: Use the quotient rule to find the derivative of 3w + w4 R (w) = %3D 2w2 + 1

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Q: Find D,y using the rules for finding derivatives. y= (sx² -2) (4x- 3x +8) Day= !!

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Q: Find the total a.f(x, y) = ex² + y² 2 derivative of t

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Q: Let y= 9 x5 – 1. Find A, B, and C so that dY = AxB + C. A В C = Then find the value of the…

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Q: Iff (x,y)=xcosy+ye*,find the second order derivative ô²f_ ô²f_ôf_ ô²f and дхду ôx² 'ôyôx' ôy²

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Q: find the equation of y where dy/dx = 3x + 5 and y= 6 when x = 0

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Q: dy Find for the equation below. dx 4x + 6Vxy = 7y³

A:

Q: find the values of the derivatives.

A: Derivative of 24-x at x=0:

Q: dy The second derivative for the function 7y + 12x = 3x² is

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Q: Calculate the derivative indicated. d²y dz? \z=8 y = where + 522 Answer:

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Q: dy Compute the derivative y' dt 4t – 7 y = 5t – 3

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Q: dy 19. What is the derivative, of the function, dx y = 3x? + 6x – 4 + 2e* – 3ln x %3D -

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Q: dy Find if X = In(sint) , y=1+cost when t = T/6. dx2

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Q: Find the indicated derivative. ? +4 y = (3t – 6)5 d t +4 %3D 5 dt ( (3t - 6)°

A:

Q: Find the derivative of the function. s(t) = 44 (8t° -5) %3D s'(1) =D 65

A: st=448t3-565

Q: Use the quotient rule to find the derivative of the following. 2x +1 y%= * +7 dy %3D xp

A: We can find the derivative by quotient rule.

Q: d²y The second derivative for the function dx? 7y + 14x = 5x² is O y' = 9 7 y' = } %3D y" = } %3D O…

A: Solution :-

Q: dy given that 2" + 2y = 2"+y. dr' Find the derivative

A: We have to find the derivative dydx, given that 2x+2y=2x+y.

Q: Calculate the derivative indicated. d'y where dx? Ix=8 y = 6- x3 + 5x?

A: An equation is given as y=6x3+5x2. The objective is to find the second derivative of the given…

Q: For the function y= 11 e 16 the second order derivative dz O lle - 32z3 O lle +32r O 12le -32z O 1le…

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Q: dy If y = (t² + 7t + 5) (2t² + 6), find dt

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Q: dy Q1: Find for the following function: dx y = sec3(/3x + 8)

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Q: dy Find the derivative, for the following. da 4. 3x + 1 y = 22 + 5

A: Given : y = 3x+1x2+54

Q: dy Q5/ a) Find 2 if y = esin (2x) dx

A:

Q: Let y= 8 x2 - 7. dy = AxB + C. dx Find A, B, and C so that %3D A = B = C = Then find the value of…

A: Given  y = 8x2-7   ......... (1) We have to find the value of A, B, and C such that dydx=AxB+C…

Q: Find D,y using the rules for finding derivatives. y = (9x² - 5) (3x² - 8x+4) Dxy=

A: Given: y = (9X2-5)(3X2-8X+4) Formula Used: Dxy = dydx ddx(uv) = dudxv+udvdx

Q: dy 6e3x using the definition of a derivative. Given Y 2e3 show that dæ

A: Given that y = 2e3x To prove that dydx = 6e3x By using  the limit definition,…

Q: Calculate the derivative indicated. d' | 1 dæ? where y = 2- + 2x? =6 6 Answer: 4x – -

A:

Q: dy Q1. By using the "definition of the derivative" find of y = v2x? dx

A: In this qus, we use tha defination of derivative of the following form

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

A:

Q: Calculate the derivative indicated.

A:

Q: d²y dæ? læ=9• Y = 7x-3+ læ? dz2

A: ddxxn=nxn-1

Q: Which of the following is the derivative of y = x² + 7? Select one: dy a. = 2x + 7 dx b. = r + 7x +C…

A: Given: y=x2+7 Since, ddxf(x)+g(x)= df(x)dx+ dg(x)dx and ddxxn=nxn-1 ; ddxconstant = 0

Q: Let y= 6 x5 − 3.Find A, B, and C so that  dy dx  = AxB + C. A = B = C = Then find the value…

A: Consider the function

Q: t3 – 3t? + 5t dt Find the general anti-derivative:

A: The solution as follows :-