Exercise · ZW-CHAIN-RULE-006 · ★★☆ Intermediate
Differentiate \(f(x)=\sqrt{1 - x^{2}}\).
Choose one option.
Show answer
- D. \(- \frac{x}{\sqrt{1 - x^{2}}}\)
Explanation
The outer function is \(F(u)=\sqrt{u}\) and the inner one is \(g(x)=1 - x^{2}\). Then \(F'(g(x))\,g'(x)=\frac{1}{2 \sqrt{1 - x^{2}}}\cdot\left(- 2 x\right)\), which gives \(- \frac{x}{\sqrt{1 - x^{2}}}\).
Review the concept: Chain rule
The chain rule gives the derivative of a composition \(f(g(x))\): the outer derivative evaluated at the inner function, times the derivative of the inner function.
\[\frac{d}{dx}f(g(x))=f'(g(x))\,g'(x)\]
More practice problems: chain rule
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- ZW-CHAIN-RULE-009 What is the derivative of e^3x?