Exercise · ZW-CHAIN-RULE-010 · ★★☆ Intermediate
Differentiate \(f(x)=\sqrt{\sin x}\).
Choose one option.
Show answer
- D. \(\frac{\cos x}{2\sqrt{\sin x}}\)
Explanation
The outer function is \(\sqrt{u}\) and the inner one is \(\sin x\). This gives \(\frac{1}{2\sqrt{\sin x}}\cdot\cos x\), the fraction with \(\cos x\) in the numerator.
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
- ZW-CHAIN-RULE-001 To differentiate sin (x^2), which is the inner function?
- ZW-CHAIN-RULE-002 Differentiate f(x)=sin x^2.
- ZW-CHAIN-RULE-003 Differentiate f(x)=(3 x + 1)^5.
- ZW-CHAIN-RULE-004 Differentiate f(x)=e^x^2.
- ZW-CHAIN-RULE-005 Differentiate f(x)=ln (x^2 + 1 ).
- ZW-CHAIN-RULE-006 Differentiate f(x)=√1 - x^2.
- ZW-CHAIN-RULE-007 Differentiate f(x)=(x^2 + x)^3.
- ZW-CHAIN-RULE-008 Differentiate f(x)=cos (ln (x^2+1)).