Find the indicated derivatives. (d)/(d x)((3 x^2)/(2)-(7)/(5 x^2))

Name: Problem 45, Chapter 2: Calculus for Business, Economics, Life Sciences, and Social Sciences
Uploaded: 2021-03-24T17:02:41-08:00
Duration: 2 min 7 s
Channel: Anurag Kumar
Description: Find the indicated derivatives. (d)/(d x)((3 x^2)/(2)-(7)/(5 x^2))

step 1 d 3x square upon 2 negative 7 upon 5 x squared upon d x so here we have to differentiate 3x squa

Find the indicated derivatives. (d)/(d x)((3 x^2)/(2)-(7)/(5...

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Key Concepts

Constant Multiple Rule

The constant multiple rule states that when a function is multiplied by a constant, its derivative is the constant multiplied by the derivative of the function. This rule allows one to easily factor and handle constants outside of the differentiation process, streamlining calculations under linear operations.

Negative Exponent Rule

The negative exponent rule is used to rewrite terms in a form that makes differentiation more straightforward using the power rule. By rewriting expressions with negative exponents, such as 1/x^n as x^(-n), one can apply the power rule directly, facilitating the differentiation process.

Differentiation

Differentiation is the process of finding the derivative of a function, which represents the rate of change of the function with respect to its independent variable. This fundamental concept in calculus is used to analyze how functions change and is critical in many applications within mathematics, physics, and engineering.

Power Rule

The power rule is a basic differentiation rule used when finding the derivative of functions of the form x^n, where n is a real number. The rule states that the derivative of x^n is n*x^(n-1). This rule simplifies the process of differentiation and is applicable even when n is a negative number or a fraction.

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