Exercise · ZW-DERIVATIVES-OF-TRIG-FUNCTIONS-008 · ★★★ Advanced
Differentiate \(f(x)=\frac{\cos {x}}{x}\).
Choose one option.
Show answer
- C. \(\frac{-x\sin {x}-\cos {x}}{x^{2}}\)
Explanation
Quotient rule: \((u/v)'=(u'v-uv')/v^{2}\) with \(u=\cos {x}\) and \(v=x\), so the numerator is \(-x\sin {x}-\cos {x}\).
Review the concept: Derivatives of trigonometric functions
These are the derivatives of sine, cosine and tangent, with angles in radians; the others follow from the quotient and chain rules.
\[(\sin x)'=\cos x,\quad(\cos x)'=-\sin x,\quad(\tan x)'=\sec^{2}x\]
More practice problems: derivatives of trigonometric functions
- ZW-DERIVATIVES-OF-TRIG-FUNCTIONS-001 Differentiate f(x)=tan x.
- ZW-DERIVATIVES-OF-TRIG-FUNCTIONS-002 Differentiate f(x)=3 sin x - 2 cos x.
- ZW-DERIVATIVES-OF-TRIG-FUNCTIONS-003 Differentiate f(x)=sec x.
- ZW-DERIVATIVES-OF-TRIG-FUNCTIONS-004 Differentiate f(x)=cot x.
- ZW-DERIVATIVES-OF-TRIG-FUNCTIONS-005 Differentiate f(x)=cos x.
- ZW-DERIVATIVES-OF-TRIG-FUNCTIONS-006 Differentiate f(x)=sin x.
- ZW-DERIVATIVES-OF-TRIG-FUNCTIONS-007 Differentiate f(x)=xsin x.
- ZW-DERIVATIVES-OF-TRIG-FUNCTIONS-009 State the derivative of csc x.
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