What is (\partial)/(\partial y)(e^{x^2y}) ?

The answer to (\partial)/(\partial y)(e^{x^2y}) is e^{x^2y}x^2

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(\partial)/(\partial y)(e^{x^2y})

\frac{\partial}{\partial y} (e^{x^{2} y})

e^{x^{2} y} x^{2}

Solution steps

\frac{\partial}{\partial y} (e^{x^{2} y})

Treat

x

as a constant

Apply the chain rule:

e^{x^{2} y} \frac{\partial}{\partial y} (x^{2} y)

= e^{x^{2} y} \frac{\partial}{\partial y} (x^{2} y)

\frac{\partial}{\partial y} (x^{2} y) = x^{2}

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

y = \frac{x - 1}{x + 1}

\int \frac{( 4 x - 11 )}{( x ^{3} - 9 x ^{2} )} d x

\frac{d}{d x} (cos (wt) + sin (wt))

\int \frac{1}{2} e^{2 x} + \frac{1}{2} d x

x^{2} + 1

What is (\partial)/(\partial y)(e^{x^2y}) ?
The answer to (\partial)/(\partial y)(e^{x^2y}) is e^{x^2y}x^2