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

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

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

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

\int_{0}^{1} x 1 - x d x

\frac{3}{2 3 x + 13}, at x = - 3

x, \frac{d ^{2} x}{d t ^{2}} + x = (t^{2} + t) sin (t)

(- 5, 11), (- 10, 6)

\frac{π}{x}

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