Question

Differentiate the function. $$F(x)=\frac{3}{4} x^{8}$$

Name: Problem 6, Chapter 3: Calculus
Uploaded: 2019-07-01T14:14:16-08:00
Duration: 58 s
Channel: Clarissa Noh
Description: Differentiate the function. F(x)=(3)/(4) x^8

   Differentiate the function.
$$F(x)=\frac{3}{4} x^{8}$$

Calculus

James Stewart 4th Edition

Chapter 3, Problem 6

Instant Answer

Solved by Expert Clarissa Noh

07/01/2019

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The function given is $ F(x) = \frac{3}{4} x^8 $. Show more…

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Differentiate the function. $$F(x)=\frac{3}{4} x^{8}$$

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Key Concepts

Power Rule

The power rule is an essential differentiation technique used for functions in the form of x^n, where n is any real number. According to the power rule, the derivative of x^n is n multiplied by x raised to the exponent (n-1), making it a quick and efficient method for differentiating polynomial expressions.

Constant Multiple Rule

The constant multiple rule is a principle in differentiation stating that the derivative of a constant multiplied by a function is equal to the constant multiplied by the derivative of the function. This simplifies the process of differentiating functions that are scaled by a constant.

Differentiation

Differentiation is the process of determining the derivative of a function, which signifies the rate at which the function's value changes with respect to changes in its input. It is a fundamental tool in calculus used to analyze and predict the behavior of dynamic systems.

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