Exercise · ZW-DERIVATIVES-OF-TRIG-FUNCTIONS-007 · ★★☆ Intermediate
Differentiate \(f(x)=x\sin {x}\).
Choose one option.
Show answer
- D. \(\sin {x}+x\cos {x}\)
Explanation
By the product rule: \((x\sin {x})'=1\cdot\sin {x}+x\cos {x}\).
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-008 Differentiate f(x)=(cos x)/(x).
- ZW-DERIVATIVES-OF-TRIG-FUNCTIONS-009 State the derivative of csc x.
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