What is implicit (e^{ex}-x^2y)=1 ?

The answer to implicit (e^{ex}-x^2y)=1 is (dy)/(dx)=-(-e^{ex+1}+2xy)/(x^2)

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implicit (e^{ex}-x^2y)=1

implicit derivative

(e^{e x} - x^{2} y) = 1

\frac{d y}{d x} = - \frac{- e ^{e x + 1} + 2 x y}{x ^{2}}

Solution steps

e^{e x} - x^{2} y = 1

Treat

y

y (x)

Differentiate both sides:

e^{e x + 1} - 2 x y - x^{2} \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{- e ^{e x + 1} + 2 x y}{x ^{2}}

\frac{d y}{d x} = - \frac{- e ^{e x + 1} + 2 x y}{x ^{2}}

\int (\frac{x ^{2} - 1}{x ^{4}}) d x

(x^{2} + 5) y^{^{'}} = x y

y = 3 x^{2}, (0, 1)

\frac{d}{d x} ((x^{3} + 9) e^{x})

\int_{2}^{7} \frac{4}{8 x - 11} d x

What is implicit (e^{ex}-x^2y)=1 ?
The answer to implicit (e^{ex}-x^2y)=1 is (dy)/(dx)=-(-e^{ex+1}+2xy)/(x^2)