Question

Find $f^{\prime}(x)$ $$ f(x)=\sin ^{2} x+\cos ^{2} x $$

   Find $f^{\prime}(x)$
$$
f(x)=\sin ^{2} x+\cos ^{2} x
$$

Calculus Early Transcendentals

Calculus Early Transcendentals

Howard Anton, Irl… 9th Edition

Chapter 2, Problem 15

Instant Answer

Solved by Expert Prakash Hampole

08/19/2020

Step 1

The Pythagorean identity states that $\sin^2x + \cos^2x = 1$ for all real numbers x. Show more…

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Find $f^{\prime}(x)$ $$ f(x)=\sin ^{2} x+\cos ^{2} x $$

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Key Concepts

Differentiation

Differentiation is the process of finding the derivative, which represents the instantaneous rate of change of a function with respect to its variable. This concept is central to calculus and is used in analyzing how functions behave, particularly in determining slopes, tangents, and rates of change at specific points.

Chain Rule

The Chain Rule is a fundamental tool in calculus for finding the derivative of composite functions. It states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the inner function, allowing for the structured differentiation of nested functions.

Trigonometric Identities

Trigonometric identities are relationships that hold true for all values within the domains of the involved trigonometric functions. These identities can simplify expressions and problems in calculus by potentially reducing complex trigonometric formulas into simpler or constant forms, thus streamlining the differentiation process.

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