find the derivative by using the definition of a derivativef(x)=4x^2+1

Q: What is the derivative of x^6

A: We have to use exponent rule.d/dx(x^n)=n*x^(n-1)

Q: Explain how to apply the First Derivative Test.

A: Explain how to apply the First Derivative Test.

Q: Compute the derivative using derivative rules that have been introduced so far y = (4 - 2x - 3x 2) 5

A: Given: y=4-2x-3x25  ……1

Q: How is this derivative found?

A: Given expression

Q: yこ(3x)2 - 5c0s x : 1(3x) |(3x)" -Scosx

A:

Q: Compute the derivative using derivative rules that have been introduced so far. y = (x 4 + 5)3

A: Given equation is y=x4+53 Applying derivative with respect to x: dydx=dx4+53dx Using the power rule…

Q: Find first derivative

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

Q: find the derivative of

A:

Q: Find derivative using product or quotient rule

A: f'(x)=((x2)'(x+3)(4x-1)-x2((x+3)(4x-1))')/((x+3)(4x-1))2       (Using quotient rule)…

Q: Find the derivative of π^2 .

A: We have to find the derivative of π2

Q: Please find the derivative using the quotient rule

A:

Q: What is the derivative of tan3x - 3tanx + 3x?

A:

Q: How to use a graph of a derivative to determine the parent function.

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Q: On which derivative rule is the Substitution Rule based?

A:

Q: 2 - x f(x) = 3 x + 1

A: given that f(x)=2-x3x+1we need to find the derivative of the functionuse the quotient rule that is…

Q: Find the derivative of   1/x^3 = 3* 1/square root of x

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Q: find anti derivative.

A:

Q: Derive the derivative function for secx and express your answer in product form.

A: ddx(secx)=ddx(1cosx)ddx(secx)=cos(x)ddx(1)-1ddx(cos(x))cos(x)2ddx(secx)=cos(x)0-1-sinxcos(x)2ddx(sec…

Q: Find the derivative of [(xt1)*] /x.

A:

Q: can you solve the derivative function or what is the corect derivative of this function?

A: We have to find derivative of given  function.

Q: find the derivative by using the definition of a derivativef(x)= the square root of x+1

A: We need to find the derivative using the first principles (without appealing to any standard…

Q: 4 6. ν- x3

A:

Q: Determine the anti derivative of the function.

A: Given Data: Function: fx=2x35+10x5-74x Similified the given function f(x).…

Q: Find the derivative. y = (lnx) 2

A:

Q: Use product rule to find the derivative of f(x) = (x2 + 5cosx)(x³ – 2x + tanx). -

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Q: What is a derivative of -2x/(x^2-1)^2?

A: Differentiate the expression -2x/(x^2-1)^2 with respect to x as follows.

Q: Compute the derivative using derivative rules that have been introduced so far       y = √(7x - 3)

A: To find the derivative: y=(7x-3) Solution: y=(7x-3) Differentiating both sides w.r.t x we get:…

Q: - Use the Quotient Rule to find the derivative of the functi

A: We apply quotient rule of derivatives .

Q: Use the Product Rule or the Quotient Rule to find the derivative of the given function.

A:

Q: Use definition of derivative to find derivative of the function f(x)=3/x+2, at x=-1

A: Given f(x)=3x+2    at x=-1To find f'(x) at x=-1

Q: Find derivative

A: Solve the following

Q: Find the second derivative of

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below

Q: Find the derivative of the function by definition. 1- V2x+3

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Q: Determine the anti derivative of the function please

A: Here given function as fx=3ex+11-x2-2sec2x-71+x2

Q: Determine the derivative of the given function by using two different methods

A: Given,         y=x2-3x2+34

Q: Find the derivative of 7-sec(x)/tan(x)

A: we have to find derivative of f(x)

Q: Use the Product Rule or the Quotient Rule to find the derivative of the function y = −x2tan x

A: Use the Product Rule or the Quotient Rule to find the derivative of the function y=-x2tan x

Q: Explain how the Second Derivative Test is used.

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

Q: Find the derivative using the long method 3-t to

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Q: Find derivative using product or quotient rule

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Q: 5. ƒ(x) = (x²+x−3)√√x²+x=3

A:

Q: State the First Derivative Test.

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Q: Find the derivative of the function without using the Quotient Rule. 4x -27 y' = ( 4x10)

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Q: Solve using applications of the derivative

A: Given problem is :

Q: Find the derivative using the definition of the equation.

A:

Q: In(x-

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Q: us to find the derivative of x) = Vt3 + 27dt -3

A:

Q: Using appropriate rule, find the 9z+3. derivative of y= 345z+9

A: