ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

derivative f(x)=x^3sin^2(x)

解

導関数

f (x) = x^{3} sin^{2} (x)

解

3 x^{2} sin^{2} (x) + sin (2 x) x^{3}

解答ステップ

\frac{d}{d x} (x^{3} sin^{2} (x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = sin^{2} (x)

= \frac{d}{d x} (x^{3}) sin^{2} (x) + \frac{d}{d x} (sin^{2} (x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (sin^{2} (x)) = sin (2 x)

= 3 x^{2} sin^{2} (x) + sin (2 x) x^{3}

グラフ

人気の例

derivative e^{3x}*sin(ln(x))

d er i v a t i v e e^{3 x} \cdot sin (ln (x))

derivative 4t^2+3t+3

d er i v a t i v e 4 t^{2} + 3 t + 3

derivative log_{10}(2-x)

d er i v a t i v e lo g_{10} (2 - x)

derivative of a*e^{2x}+b*e^{-3x}+c*e^x

\frac{d}{d x} (a \cdot e^{2 x} + b \cdot e^{- 3 x} + c \cdot e^{x})

d/(dt)(cos^4(t)-sin^4(t))

\frac{d}{d t} (cos^{4} (t) - sin^{4} (t))