Find the derivative of each function. (a) f(x)=sinx^2 (b) f(x)=sin^2 x (c) f(x)=sin2 x

Name: Problem 19, Chapter 2: Calculus: Early Transcendental Functions
Uploaded: 2022-03-03T14:41:05-08:00
Duration: 1 min 52 s
Channel: Lauren Shelton
Description: Find the derivative of each function. (a) f(x)=sinx^2 (b) f(x)=sin^2 x (c) f(x)=sin2 x

step 1 Okay, so each of these derivatives will involve the chain rule, but each chain rule will look a

Find the derivative of each function. (a) f(x)=sinx^2 (b)...

Key Concepts

Chain Rule

The chain rule is a fundamental technique in differentiation used to find the derivative of composite functions. When a function is composed of two or more functions, the derivative of the outer function is evaluated at the inner function and then multiplied by the derivative of the inner function.

Basic Trigonometric Derivatives

Knowledge of the derivatives of basic trigonometric functions, such as sin(x) and cos(x), is essential. For example, the derivative of sin(x) is cos(x), and these results are frequently applied when differentiating more complex trigonometric expressions.

Power Rule

The power rule is a basic differentiation rule stating that the derivative of x^n is n*x^(n-1) for any real number n. This rule is especially useful when dealing with functions that involve polynomial powers, and it often works in tandem with the chain rule.

Constant Multiple Rule

The constant multiple rule in differentiation states that a constant coefficient can be factored out of the derivative. In other words, if a function is multiplied by a constant, the derivative of the product is that constant multiplied by the derivative of the function.

Differentiation of Composite Functions

Differentiating composite functions involves applying multiple differentiation rules in succession, such as the chain rule, power rule, and the basic derivatives of elementary functions. Recognizing the structure of a composite function is key to effectively applying the appropriate rules.

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