Find the derivative of 1 f(x) || 1+ Vx using the definition of derivative. State the domain of the function and the domain of its derivative.

Q: Find the derivative (f' (x)) of f(x) = Vx + 2 . %3D

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Q: Use the definition of the derivative equation (f(x+h)-f(x))/h) to find the derivative of (1/x).

A: The definition of derivative is given by,

Q: Find the derivative of the function. A) f(x) = In(x*Vx² - 3)

A: This problem can be solved by using the Chain rule as explained in step 2.

Q: と FCx) = 1oga x-1 %3D

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Q: Find the derivative of the algebraic function.

A: To find the derivative of the algebraic function. f(x)=3x-1x

Q: Find the derivative of the function. f(x) = ex In(x³) f'(x) = X

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Q: Find the derivative of the function by using the rules of differentiation. 1 f(x) = f'(x) =

A: topic - derivative of a function

Q: 2 f(x) = ; 2x-1

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Q: Find the derivative of the function.

A: Given function is: f(x) = [ln (2x)]3 We have to find the derivative of the function.

Q: Calculate the derivative of f(x)=4x³ with respect to x and evaluate this derivative at x=2.

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Q: Find f'(x) using the definition of the derivative. 1. f(x)=x^3-1

A: We have given f(x) = x3-1 So using definition of derivative  f'(x) = limh→0fx+h-fxh So f(x+h) =…

Q: Find the derivative of the function f (x)=x-2r.

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Q: Find the derivative of F(x) = 1 / (3x+1) directly from the definition of the derivative:

A: Here the question itself need to use definition of derivative to find out the derivative of given…

Q: Use the alternate form of the derivative to find the derivative at x=c, if it exists f (x) = x3 +…

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Q: Find the derivative of f(x) = 2e%.

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Q: Q1. Find the derivative of f(x) = 2x -- by using the definition of derivative.

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Q: Find the derivative of the function f by using the rules of differentiation. f(x) = (1 + 3x²)² + 2x³…

A: The given function is fx=1+3x22+2x3.

Q: Use the alternate form of the derivative to find the derivative at x=c, if it exists. f(x) = x³ +…

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Q: Use the DEFINITION OF A DERIVATIVE to find the derivative of the function. 5) f(x) = 2x2 at x 1 %3D

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Q: Find the derivative of the function. g(x) = (sech(8x)) g'(x) = %3D

A: take derivative

Q: Find the derivative of the function y=x2+3x+1x without using the quotient rule for the derivative.

A: Given: y=x2+3x+x we know that ddxxn=nxn-1

Q: Use the alternate form of the derivative to find the derivative at x-c, if it exists. f(x) = x³ +2x2…

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Q: Give the derivative formula for the function g(x) 2.1X 2 g '(x)

A: The given function is

Q: Find the derivative of the function. f(x) = In(x + V2 + x²) f '(x) =

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Q: Find the derivative of f (x) = 1x , x = 0.

A: Given: f(x)=x at x=0

Q: Find the derivative of the function f(x) = 8x2 – 13x by the definition of derivatives f(x + h) –…

A: on using this formula we get = 16x-13

Q: Use the definition of the derivative to find the derivative of, f(x)=6

A: topic - derivatives

Q: Use the rules of differentiation to find the derivative of the function.

A: Given,

Q: Use the Quotient Rule to find the derivative of the function. x2 h(x) = %3D X + 2 h'(x) =

A:

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 using the first principle  F(x)= (x-1)(x-2)

A: Given F(x)=(x-1)(x-2) To find the derivative using the first principle From the first principle, we…

Q: Find the Derivative of the function f by using the rules of differentiation F(x) = x^3+4x^2 + x -4…

A: Power rule:ddxxn=n xn-1ddxx=1

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

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Q: Consider the function f(x)= x^2−3x.   Compute the derivative using the definition

A: In order to solve this question we will use the concept of first principle which defines derivative.

Q: Find the derivative of the function ° (2x + 1) f(x) = In x2 – 3 -

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Q: Find the derivative of the algebraic function.

A: Given algebraic function fx=3x-1x. Differentiating the given function with respect to x,…

Q: Use the General Power Rule to find the derivative of the function. g(x) = V7- Sx

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Q: o f(x) = 4~/x+3

A: by using definition of a derivative.

Q: Find the f derivative of x given f(x)=(3x)^-1

A: Calculation:Compute the derivative of f(x) = (3x)−1 as follows.

Q: Use the definition of the derivative to find the derivative of f(x)=8x+0 f^1 (x)=

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Q: Q1. Find the derivative of f(x) = 2x² -- by using the definition of derivative.

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Q: Find the derivative of the function f by using the rules of differentiation. f(x) = x6

A: Power rule: ddxxn=nxn-1

Q: Find the derivative of the function. f(x) = (x² + 8) In(x) f'(x) =

A: In this question we need to find a derivative of the given function

Q: Find the derivative of f(x) = x3 + 2x, use the definition of the derivative

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Q: Find the derivative of the function.

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Q: Find f (x) of f(x)= by using the definition of the x- derivative.

A: Definition of Derivative is given as

Q: Find the derivative of f (x)= 2- √(5x) using the definition of derivative.

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Q: Use the General Power Rule to find the derivative of the function. g(x) = V3 - 9x %3D g'(x) =

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Q: Find the derivative of the function f(x) = /(x³+ 11x) by using the definition of the derivative.

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

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: