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人気のある微分積分 >

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

解

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

解

\frac{d}{d x} (f (x)) sin (x) + cos (x) f (x)

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (sin (x)) = cos (x)

= \frac{d}{d x} (f (x)) sin (x) + cos (x) f (x)

人気の例

derivative of xln(sin(x))

\frac{d}{d x} (x ln (sin (x)))

integral from 0 to infinity of e^{-x}

\int_{0}^{\infty} e^{- x} d x

integral of xcos(x^2)

\int x cos (x^{2}) d x

derivative f(x)=9+3/x

d er i v a t i v e f (x) = 9 + \frac{3}{x}

integral of (x/(x^2+4))

\int (\frac{x}{x ^{2} + 4}) d x