4) Use the quotient rule to find the derivative. Simplify the result. d [3+7e* dx | 6e* + 5

Q: y = 3 sin 3X tan 2x

A:

Q: Find the derivative of g(x) = In(sin²(ed/x)).

A:

Q: Find the derivative. d. (In (9x? + 4)) dx di (In (9x? + 4)) =| dx

A: Solution:To find:ddx ln (9x2+4)=?Formula:ddx(log x)=1xddx(xn)=nxn-1

Q: Find the derivatives of the function defined as follows. y = -6x4 sin 6x

A: Given equation - y =-6x4sin6x                    .................(1)Differentiating on both sides…

Q: Find the derivative of the trigonometric function.

A: To find the derivative of the trigonometric function.  y=csc1-2x2

Q: Use the Power Rule to compute the derivative.

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

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = (2…

A: Given function is   Differentiating both sides with respect to x, we get

Q: 2 dx (1+x²)3/2

A:

Q: Calculate the following derivative: d а.) dx (In(tan(2x)) + 3sinx)

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Q: Use the first principles to find the derivative of cos(x -4x).

A: By the first principle  f'(x)=limh→0f(x+h)-f(x)h. So, dcosx2-4xdx=limh→0cosx+h2-4x+h-cosx2-4xh…

Q: 3x-4 1. Y= Arctan 4

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Q: Find the derivative of the trigonometric function. y = 4 sin(3nx)

A: The given function is: y=4sin3πx   We know that; The Power law: ddxxn=nxn-1 The chain rule:…

Q: f(x) = e2 sin¯+(3x) + In (cosh-1(e³x))

A:

Q: Discuss the relationship between the derivative dy/dx and (Lim) with drawing if it is required ?

A: See the attachment

Q: Use the quotient rule to find the derivative of the following. (2x +2) (3x + 7) y = 8x-7 dy dx %3D

A: The given function,y=(2x2+2)(3x+7)8x-7

Q: 4) Use the quotient rule to find the derivative. Simplify the result. d dx |3x – 4

A:

Q: find the second derivative and simplify the final result 4. y= 5/ (sin3x + cos3x)

A: y=5sin3x+cos3x Differentiating with respect to x, we get…

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given, y=coshtan-13x

Q: What is the derivative of cos2t

A: Formulas used

Q: The derivative of sec22x(cos2x−sin2x) with respect to x is?

A: I have appended the formula used in the solution part of the question

Q: Find the derivative of the trigonometric function. y = 6 sin(3nx)

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Q: Using appropriate rules, find the derivative of y = x²e4# + sin(4x? + 6x)

A:

Q: use the Power Rule to compute the derivative.

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

Q: What is the derivative of sin(2x) at the point (0,0)? O 2 O -2 O 4

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Q: find the derivative of f(x) = cos(sin(4x+7)^4). simplify

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Q: (a) Find the derivative of the function g(x) = sin2 x + cos2 x (b) then use a trigonometric…

A:

Q: В. f(x) = (sin ebx³ ). 3 |cot(26x) x4 -

A:

Q: Find the derivative of g(t) = tan(5 - sin 2t).

A: Given function is gt=tan5-sin2t. To find the derivative of the function. Solution: Chain rule of…

Q: Find the derivative of ?(?) = 6 sec2(7x? − 3).

A: Follow the procedure given below.

Q: Find the derivative and don't simplify the answer. y=tan-1(5x4)+(cos-1(x))6

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Q: g(x)%3Dx sin(2*)

A:

Q: ) Find the derivative of the following: a) sin (4x- 7x+ 3)

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Use the quotient rule and the derivatives of the sine and cosine functions to prove that d/dx (cot…

A: we have to find the derivative of the given  expression by using quotient rule

Q: Find each derivative : Dx[cos(3x)]=-sin(3x).Dx(3x)=-3 sin 3x

A: Find each derivative : Dx[cos(3x)]=-sin(3x).Dx(3x)=-3 sin 3x

Q: # 49. y = 2x arccos r -2/1- x2

A: Given y=2x arccosx-21-x2

Q: (A) Find the first derivative of the following function: 1+ cos2x f(x) = %3D 1- cos2x |

A:

Q: cosx sin x +cosX

A:

Q: Use the rule for reciprocals (수) - - to find the derivative: d 1 %3D dx lx2 Зх + 2

A: Given the rule of reciprocals as 1f'=-f'f2. It is required to find the derivative of 1x2-3x+2. Note…

Q: Find the derivative of the following function. y= -58x2-3 %3D dx

A: Simply finding the derivative of the function gives us the answer.

Q: find the derivative and simplify the answer sin² (esin t) + cos-{(2t3 – 5)

A:

Q: Find the derivative and simply. 1+cosx (a) f(x) = 1-cosx

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Use the Power Rule to compute the derivative.

A:

Q: Find the derivative of flx)=Sin(7x'+91Cos(3x?)

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Q: • S arcsin(/x) dx

A:

Q: Find the derivatives of the functions y = 3/(5x2 + sin 2x)3/2

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Q: Find the derivative. d 3x +1 In xp Зх- 1 Зх + In dx 3x-

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Q: Find the derivative of: 8 sin? ( – 9x*). - Hint: sin? (x) = [sin(x)]*..s ..so use the chain rule…

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Q: Find the derivative of the function f(x) = x sin(6x + 14)+ In(5z+9) Answer:

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Q: Find the derivative. sint 1 du 16-u? 미행

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Q: Please solve and simplify

A: Simplify the given function as follows.