a) Use the Product Rule to find the derivative of the given function. b) Find the derivative by multiplying the expressions first. F(x) = 7x° (x* - 9x)

Q: Use formulas (1) and (2) and the power rule to find the derivatives of f (x) =3x/4 - 2

A: As the formulas (1) and (2) are not provided here. So, I solved by using the basic formulas of…

Q: 2. By differentiation rules , evaluate the derivatives of the following and simplify as possible:…

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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: Use formulas (1) and (2) and the power rule to find the derivatives of f (x) = -2x

A: To find the derivative of: f(x)=-2x Solution: f(x)=-2xOn differentiating both sides w.r.t x we…

Q: Find the derivative of the trigonometric function.

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

Q: 2 dx (1+x²)3/2

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Q: Find the derivative of the function by using the Quotient Rule. Simplify your answer. x2. - 4x + 3…

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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: Use the definition of the derivative to find the value of f'(2) if f(x)=x'-2x. Then use it to write…

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Q: .2 19) y=x² In 4x

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Q: Find the derivative, the slope of the tangent line, and the equation of the tangent line at the…

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Q: Find the derivative  f(x)= sin 2xcos2x

A: The given function is,

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: Use formulas (1) and (2) and the power rule to find the derivatives of f (x) = 2x - 6/7

A: Explanation: Given that,  f(x)=2x-67

Q: Find the derivative of the trigonometric function. g(x) = 8 tan(9x) g'(x) =

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Q: Use the definition of the derivative to find the derivative of the function h(x) = x+3 then find the…

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Q: Use formulas (1) and (2) and the power rule to find the derivatives of f (x) = 1/x3

A: Definition used -                     1am=a-m            Power rule of derivative -…

Q: Find the derivative y', where (3 – x) (3+x)2 3 %3D 1 - x

A: Given function is y=x21-x 3-x3+x23

Q: Find the derivative of the trigonometric function. g(x) = 9 tan(2x)

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Q: Find the derivative of the function f(x) = 7x sin(4x).

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Q: Write the first and second derivatives of the function. f(x) = x3 - 9x2 + 27x f'(x) - 18x + 27 f"(x)…

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Q: Use formulas (1) and (2) and the power rule to find the derivatives of f (x) = x2/3

A: The function: fx=x23

Q: Use the product rule to find the derivative. Simplify the result. d [(3x + 7)(x² + 2x)] dx

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

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Q: Find the derivative of the function. Simplify and express the answer using positive exponents only.…

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Q: Find the derivative of the function In (2x+10) f (x) = x* sin (7x + 14) +

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A: Proceed as shown below

Q: Find the derivative of the function. y = 2 sin4(4x2)

A: y = 2 sin4(4x2) dy/dx = ?   Useful formulas:ddx xn = nxn-1ddxsin(x) = cosx

Q: Find the derivative of the function f(x) = / (x³ + 7x) by using the definition of the V derivative.

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Q: -1 2.) у %3D tan -6.x4

A: To differentiate: y=tan-1(-6x4) Solution: We know, ddx(f(g(x)))=f'(g(x)).g'(x)…

Q: 23: USE THE DEFINITION OF THE DERIVATIVE to find the derivative: :9(x)=3

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Q: Find the derivative of the trigonometric function.   y = csc(1 − 2x)2

A: the given function is: y=csc1-2x2 we have to find the derivative of the given function.

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: Compute the derivative of the given function in two different ways. x3 h(x) = + 8x2 6x2 g· f' – f ·…

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Q: Find the derivative of the function f(x) = 2x3 – 3x by using the definition of the derivative.

A: By using the definition of derivative of a function, we differentiate the given polynomial as in…

Q: Use the rules of differentiation to find the derivative of the function. y=9x². + 7 sin x

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Q: Use the chain rule to find the derivative of 3e^ 8x^7−6x^6 Use e^x for exex.

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Q: Calculate the derivative of the function, then find the value of the derivative at the specified…

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Q: Find the derivative of the function In(4x+10) f(x) = x* sin(9x + 12) +

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Q: Use the rules of differentiation to find the derivative of the function. y = 9x4 + 2 sin x y' =

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Q: Assuming that the equation -2x?y² + 3y sin(x) = 38 gives y implicitly as a function of x, find the…

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Q: Use the definition of the derivative to find the derivative of each function with respect to x 1)…

A: Given: y= -2x+5

Q: Use the definition of the derivative to find the derivative of the function g(x) = 4 –x², then find…

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Q: Find the derivatives of the functions y = x2 sin2 (2x2)

A: Given that : The function is y = x2 sin2 ( 2x2 ) .

Q: Write the first and second derivatives of the function. f(x) = x3 - 6x² + 29x f'(x) f"(x) Use the…

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Q: 2 y = 3x³+=+6x X

A: We use the formula as given below:

Q: Find the derivative of the function. Simplify and express the answer using positive exponents only.…

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Q: Find the derivative of the function (5x? +sin2xj3/2

A: Given: The function is, y=35x2+sin2x32. The objective is to find the derivative of the function.

Q: f(x)=4 sin¹+x+√4x²

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Q: (c) For y = 2x2 In(4x) – x², find y'.

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