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

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

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

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

x^{2} e^{y z^{2}} \cdot 2 yz

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x^{2} e^{y z^{2}} \cdot 2 yz

\frac{d x}{d y} = 70 - 4 x

\int_{3}^{\infty} e^{- 7 x} d x

x \to 7 - lim (\frac{4}{( x - 7 ) ^{2}})

y = - 6 x + k

\int_{0}^{1} 1 (x^{2} + 1) e^{- x} d x

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