Use the definition of the derivative to differentiate each function.

Q: Find the derivative of the function f(x)=arccsc(7x)

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Q: F(X) = X + よ2 %3D

A: Given, fx=x+3x2

Q: Use the definition of the derivative to differentiate the following function.    f(x) =1/2x^2+ 5.…

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Q: Use the Product Rule or Quotient Rule to find the derivative. f(x) = x³ (x* + 1)

A: Here we use Product Rule of differentiation.   If f and g are both differentiable, then ddxf(x)·g(x)…

Q: Use the Quotient Rule to find the derivative of the function. f(x) = f'(x) =

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Q: Use various notations for the derivative

A: Solution: There are four popular derivative notations : (1) Leibniz Notation (2) Lagrange Notation…

Q: f(x) =

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Q: Use the power rule to find the derivative of f(x) = x – 14

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

A: Given :           The function h(x) = xx3 + 1 To find the derivative of h(x) using product rule.

Q: Use the Quotient Rule to find the derivative of the function.                           h(x) =…

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Q: Explain in words how to evaluate the derivative of function?

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Q: Find the derivative of the function without using the Quotient Rule. y 63 8(x)10

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Q: determine

A: We will find the derivative using product rule and chain rule.

Q: Use the derivative to explain why the function f(x) = x³ + x³ is a one to one %3D function.

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Q: Use the Quotient Rule to find the derivative of the function. f'(x) = f(x) x X-5

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Q: find the derivative of each function

A: To Find: The derivative of  18. fx=2x2-3x3919. fx=x3-5x2-320. fx=13x2-6x+2

Q: Use the definition to compute the derivative of the function f (x) = Vx2 + 1.

A: We have to find derivative

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

A: Differentiation of the function f(x) helps to find the derivative of the function. The given…

Q: If f(x) = use the definition of the derivative to find f.

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Q: Use the definition of a derivative to find ƒ'(x). f(x) = 9 f'(x) = Preview

A: Consider the function  fx=9

Q: Use the Product Rule or the Quotient Rule to find the derivative of the function f(x) = (x2 + x −…

A: Let, u=x2+x-1u'=2x+1Let, v=x2-1v'=2x

Q: compute the derivative. f (x) = esin2x

A: Differentiation of the function with respect to x helps to find the derivative of the function. The…

Q: Use the definition of the derivative to differentiate the following function. x2 f(x) = 3+ x

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Q: Use definition to find the derivative of the function f (x) = 5x- 2x at = 3. [2 Marks] %3D

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

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx The quotient rule of…

Q: calculate the derivative. f (x) = 3ex − x3

A: To calculate the derivative. f (x) = 3ex − x3

Q: Use the definition of the derivative to differentiate the following function. 1 f(x) = x² – 2 -

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

A: topic - derivatives

Q: Find the derivative of the function, Simplity andexpress the answer positive exponents only. using

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Q: Use the Quotient Rule to find the derivative of the function.…

A: Given function is fx=xx-5 To find the derivative of the function using Quotient rule. Solution:…

Q: Use the rules of differentiation to find the derivative of the function. y = x12

A: The given function is y=x12 rule used: ddxxn=nxn-1

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

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Q: Write the definition of the derivative of f (x).

A: Two types of derivatives are defined 1) LHD -  Left Hand Derivative 2) RHD - Right Hand Derivative…

Q: find the derivative of the function: sqrt(x/(x+1))

A: topic - derivative of a function

Q: Let ƒ(x) = x2, Find the derivative

A: ddxxn=n xn-1

Q: F(x) = X2

A: Consider the function: fx=x2 The derivative of f(x) with respect to x is the function f′(x) and is…

Q: F(x) = X

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: 1/3 for

A: Answer

Q: Find the derivative F

A: To find the derivative

Q: F(x) = Vx +3x %3D

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: Use the definition of a derivative to find f ′ (x). f (x) = 2 − 3x

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Q: Use the definition of derivative to find f (x) if f(x) = Vx+3.

A: fx=x+3

Q: Use the definition of the derivative of find (sin x)'.

A: 1)

Q: Use the derivative definition,

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Q: Use the definition of the derivative of a function to determine f'(x) where f(x)=-

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Q: Find the derivative of the function without using the Quotient Rule. y = 63 8(x)10

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Q: Use the rules of differentiation to find the derivative of the function. f(x) = −9

A: Given, f(x) = −9   To evaluate f'(x)=?

Q: Complete the table to find the derivative of the function without using the Quotient Rule.

A: Here given function as y=2xx13 Use the formula of quotient rule of the derivative.…

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: