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

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

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(\partial)/(\partial y)(z^2e^{xy})

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

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

Solution steps

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

Treat

z, x

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

y^{^{''}} + 16 y^{^{'}} + 65 y = 0

\frac{d}{d x} (x^{2} - 25 ln (x^{2}))

f (x) = \frac{x}{x ^{2} - 6}

\int_{- 3}^{0} - x^{2} - 3 x d x

\int coth (x) d x

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