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

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

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

implicit

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

Solution steps

x y + 7 ey = 7 e

Treat

y

y (x)

Implicit Derivative

\frac{d y}{d x}

x y + 7 ey = 7 e : - \frac{y}{x + 7 e}

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

Implicit Derivative

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

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

Substitute

\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}}

What is implicit (d^2y)/(dx^2),xy+7ey(x)=7e ?
The answer to implicit (d^2y)/(dx^2),xy+7ey(x)=7e is (d^2y)/(dx^2)=(2y)/((x+7e)^2)