If f(x)=sin^2 x, find f^'''(x) (A) -sin^2 x (B) cos2 x (C) -4 sin2 x (D) -sin2 x

Name: Problem 21, Chapter :
Uploaded: 2019-08-28T23:21:54-08:00
Duration: 41 s
Channel: Amrita Bhasin
Description: If f(x)=sin^2 x, find f^'''(x) (A) -sin^2 x (B) cos2 x (C) -4 sin2 x (D) -sin2 x

step 1 Let us check the chain rule. First derivative, F prime of x, 2. sine x, cosine x. But we don't s

If f(x)=sin^2 x, find f^'''(x) (A) -sin^2 x (B) cos2 x (C)...

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Key Concepts

Differentiation of Trigonometric Functions

This concept involves understanding how to differentiate trigonometric functions like sine and cosine. It is essential to know that the derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x), which forms the basis for differentiating more complex trigonometric expressions.

Chain Rule

The chain rule is a fundamental technique in calculus used to differentiate composite functions. It allows you to compute derivatives of functions where one function is nested within another by multiplying the derivative of the outer function evaluated at the inner function by the derivative of the inner function.

Higher-Order Derivatives

Higher-order derivatives refer to the repeated application of differentiation on a function. For example, finding the third derivative involves differentiating the function three times. This concept is important for understanding the behavior of functions beyond the first derivative, such as their curvature and acceleration.

Trigonometric Identities

Trigonometric identities, such as the double-angle identities, are useful tools for simplifying trigonometric expressions before or after differentiation. They help in rewriting functions into more manageable forms, which can simplify the process of differentiation and the interpretation of results.

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