QuestionMarch 3, 2026

If f(x)=sin^3x find f'(x) square Find f'(4) square

If f(x)=sin^3x find f'(x) square Find f'(4) square
If f(x)=sin^3x find f'(x) square Find f'(4) square

Solution
4.3(278 votes)

Answer

f'(x) = 3\sin^2 x \cdot \cos x ### f'(4) \approx -1.121 Explanation 1. Differentiate f(x) f(x) = \sin^3 x can be written as (\sin x)^3. Using chain rule: **\frac{d}{dx}[\sin^3 x] = 3\sin^2 x \cdot \cos x** 2. Compute f'(4) Substituting x = 4: f'(4) = 3\sin^2(4) \cdot \cos(4) 3. Evaluate numerically \sin(4) \approx -0.7568, \cos(4) \approx -0.6536 \sin^2(4) \approx 0.5727 f'(4) \approx 3 \times 0.5727 \times (-0.6536) \approx -1.121

Explanation

1. Differentiate $f(x)$ <br /> $f(x) = \sin^3 x$ can be written as $(\sin x)^3$. Using chain rule: <br />**$\frac{d}{dx}[\sin^3 x] = 3\sin^2 x \cdot \cos x$** <br /><br />2. Compute $f'(4)$ <br /> Substituting $x = 4$: <br />$f'(4) = 3\sin^2(4) \cdot \cos(4)$ <br /><br />3. Evaluate numerically <br /> $\sin(4) \approx -0.7568$, $\cos(4) \approx -0.6536$ <br />$\sin^2(4) \approx 0.5727$ <br />$f'(4) \approx 3 \times 0.5727 \times (-0.6536) \approx -1.121$
Click to rate:

Similar Questions