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受欢迎的微积分 >

implicit (d^2y)/(dx^2),xy+7ey(x)=7e

解答

隐函数求导

\frac{d ^{2} y}{d x ^{2}}, x y + 7 ey (x) = 7 e

解答

\frac{d ^{2} y}{d x ^{2}} = \frac{2 y}{( x + 7 e ) ^{2}}

求解步骤

x y + 7 ey = 7 e

将

y

视为

y (x)

隐函数

x y + 7 ey = 7 e

的导数:

- \frac{y}{x + 7 e}

\frac{d y}{d x} = - \frac{y}{x + 7 e}

隐函数

\frac{d y}{d x} = - \frac{y}{x + 7 e}

的导数:

- \frac{\frac{d y}{d x} ( x + 7 e ) - y}{( x + 7 e ) ^{2}}

\frac{d ^{2} y}{d x ^{2}} = - \frac{\frac{d y}{d x} ( x + 7 e ) - y}{( x + 7 e ) ^{2}}

替代

\frac{d y}{d x} = - \frac{y}{x + 7 e} : \frac{2 y}{( x + 7 e ) ^{2}}

\frac{d ^{2} y}{d x ^{2}} = \frac{2 y}{( x + 7 e ) ^{2}}

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\int \frac{x}{x ^{2} - 16} d x

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(x + y) \frac{d y}{d x} = 1

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