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人気のある微分積分 >

derivative of e^{x^4y}

解

\frac{d}{d x} (e^{x^{4} y})

解

e^{x^{4} y} (4 x^{3} y + \frac{d y}{d x} x^{4})

解答ステップ

\frac{d}{d x} (e^{x^{4} y})

連鎖法則を適用:

e^{x^{4} y} \frac{d}{d x} (x^{4} y)

= e^{x^{4} y} \frac{d}{d x} (x^{4} y)

\frac{d}{d x} (x^{4} y) = 4 x^{3} y + \frac{d y}{d x} x^{4}

= e^{x^{4} y} (4 x^{3} y + \frac{d y}{d x} x^{4})

人気の例

integral of x^3(5+x^4)^{11}

\int x^{3} (5 + x^{4})^{11} d x

integral from x^3 to x^4 of (2t-1)^3

\int_{x^{3}}^{x^{4}} (2 t - 1)^{3} d t

integral of (sqrt(3))

\int (3) d x

derivative f(x)=(60)/(0.01x^2+1)

d er i v a t i v e f (x) = \frac{60}{0.01 x ^{2} + 1}

derivative of arctan(x^2+1)

\frac{d}{d x} (arctan (x^{2} + 1))