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人気のある微分積分 >

derivative of {f}(x{g}(x))

解

\frac{d}{d x} (f (x) g (x))

解

\frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x)

解答ステップ

\frac{d}{d x} (f (x) g (x))

積の法則を適用:

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

f = f (x), g = g (x)

= \frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x)

= \frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x)

人気の例

derivative y/(y+a/y)

d er i v a t i v e \frac{y}{y + \frac{a}{y}}

sum from n=0 to infinity of n/(e^{2n)}

n = 0 \sum \infty \frac{n}{e ^{2 n}}

integral of (e^{4x}-e^{2x}+1)/(e^x)

\int \frac{e ^{4 x} - e ^{2 x} + 1}{e ^{x}} d x

y^{^{'}} = y

derivative f(x)=4sqrt(x)-6

d er i v a t i v e f (x) = 4 x - 6