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人気のある微分積分 >

(d^2)/(dx^2)(xy)

解

\frac{d ^{2}}{d x ^{2}} (x y)

解

2 \frac{d y}{d x} + x \frac{d ^{2} y}{d x ^{2}}

解答ステップ

\frac{d ^{2}}{d x ^{2}} (x y)

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

= \frac{d}{d x} (y + x \frac{d y}{d x})

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

= 2 \frac{d y}{d x} + x \frac{d ^{2} y}{d x ^{2}}

人気の例

integral from 0 to ln(4) of e^x-e^{-3x}

\int_{0}^{l n (4)} e^{x} - e^{- 3 x} d x

limit as x approaches+0 of (tan(x)-x)/x

x \to + 0 lim (\frac{tan ( x ) - x}{x})

integral from-2 to 2 of (x+3)sqrt(4-x^2)

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

derivative f(x)=sqrt(2e^{x^3)+1}

d er i v a t i v e f (x) = 2 e^{x^{3}} + 1

derivative of sqrt(x)+5e^x

\frac{d}{d x} (x + 5 e^{x})