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

The answer to (\partial)/(\partial y)(x^2e^{x^2y}) is e^{x^2y}x^4

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

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

e^{x^{2} y} x^{4}

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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}

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

Simplify

x^{2} e^{x^{2} y} x^{2} : e^{x^{2} y} x^{4}

= e^{x^{2} y} x^{4}

ln (x^{2} - 8 x + 1) (8)

\frac{d}{d x} (e^{x} - 2 sin (x))

\int (\frac{cot ^{2} ( x )}{cos ^{2} ( x )}) d x

\frac{( \frac{10}{6} )}{s ( s ^{2} + \frac{1}{2} )}

\frac{5}{6 x ^{5}}

What is (\partial)/(\partial y)(x^2e^{x^2y}) ?
The answer to (\partial)/(\partial y)(x^2e^{x^2y}) is e^{x^2y}x^4