Find the derivative of the function using the definition of derivative. f(x) = 8x4 f'(x) = State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.)

Q: Find the derivative of the function  y = ln (8x3-x2)

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Q: Find the derivative of the function by definition 1 1- f(x) = 2x +3

A: Given f(x) = 12x+3 Consider f'(x) = limh→0f(x+h)-f(x)h= limh→012(x+h)+3-12x+3h=…

Q: Find the derivative of the function by using the rules of differentiation. f(x) = −5x2

A: The power rule of differentiation states that the derivative of ddxxn=nxn-1. The main objective is…

Q: derivative of the function f (x) = xsec-1 (2x + 1)

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Q: Find the derivative of 1 f(x) || 1+ Vx using the definition of derivative. State the domain of the…

A: We have to find the derivative of the given function by using the definition of derivative.

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

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Q: Find the derivative of the function. 5 F(x) 1 + 4x + x3 F'(x) :

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Q: Find the derivative of the function. h(x) = ex² - > x + 5 %3D

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Q: Find the derivative of the function using the definition of derivative. 1 g(x) 8 + Vx g'(x) =

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Q: Find the derivative of the function. X-1

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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: Find the derivative of the function. f(x) = 8x

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Q: Find the derivative of f(x)=[sin(3x)]^3

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Q: Find the derivative of the function. Express it using positive exponents only. y…

A: For power 3, use the power rule. Then use the chain rule

Q: Find the derivative of the function by using the rules of differentiation. f(x) =    3/x3 + 8/√x + 3

A: Given function is

Q: Find the derivative of the function using the definition of derivative. f(x) = rx + q

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Q: Find the derivative of the function.

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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: Find the derivative of the function.

A: Given function is hx=x+5x2+32 We have to find derivative of given function. To find derivative of…

Q: Find the derivative of the function using the definition of derivative. 1 f(x) x² - 36

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Q: Find the derivative of the function f(x)=x-2/2+x square root

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Q: Can you help me step by step with this problem?

A: Let's assume u = 3 + xsecxPlease note that the second term is made up of two functions of x and they…

Q: Find the derivative of the function. 10 f(x) = 3 + 2cos x

A: Recall: dxndx=n xn-1 d(cos ax)dx= a(- sin ax) dc1f(x)±c2 g(x) dx= c1d[f(x)]dx± c2d[g(x)]dx

Q: y=x²

A: I have stated the used formula in the solution

Q: Find the relative extrema of the function f(x)= x2+3x+4 using first derivative test.

A: fx=x2+3x+4 To find extrema of function.

Q: Find the derivative of the function g(x)=x3∫x2tdt.

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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 curve f(x) = 3x² - 6x + 1. Use the result to find the slope of the…

A: Follow the procedure given below.

Q: Find the derivative of the function f(x)=2x−73x−2 at x=2

A: topic - derivative of a function

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 f(x)=2/3x

A: Given is fx=23x. Power rule of differentiation states that: ddxxn=nxn-1 Differentiating the given…

Q: Find the derivative of the function and evaluate the derivative at the given x-value. f(x) = 5x +x…

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Q: find the derivative of the function f(x)=6x

A: We have to find the derivative of given function.

Q: find the derivative of the function f(x)=x^3+2x at -3

A: find the derivative of the function f(x)

Q: Find the first derivative of f (x) = 2* 2*

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Q: Find the derivative of x²e*.

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

A: by using definition of a derivative.

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 f(x)=x2-3x. Use the result to find the slope of the tangent line to the curve…

A: Given: fx=x2-3x To Find: The derivative of the given function and the slope of the tangent line at…

Q: Find the derivative of the function and then evaluate at the given point. y = 2x² - 3x: (-1,5)

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Q: Find the derivative of the function using implicit differentiation.  1.) x³-3x²y+2xy²=12 2.) x²-y²…

A: This question is related to implicit differentiation, We will solve it using given information.

Q: Find the derivative of the function f by using the rules of differentiation. 4x2 + x 4 + f(x) f'(x)…

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Q: Find the derivative of the function   f(x)=ln(x3(2x+1)/x^2−3)

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Q: 2) Find the derivative of the function f(x) = 3x² by definition

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Q: Find the derivative of the function: f(x)=ln  (x-3)^2÷(2x-1)^3

A: Given function is,

Q: find the derivative of the given function. f(x)= 3x2- sin(x)/x

A: Given

Q: Find all possible functions with the given derivative. = రx = 1x 2x

A: The answer is given below

Q: function

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Q: Find the derivative of the function. (2x

A: In the given question, the fundamental theorem of calculus is applied. The fundamental theorem of…

Q: Find the derivative of the given function by using definition of derivative  f(x)= sec(x)

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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: