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

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

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

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

- e^{- yz} x^{2} z

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

e^{- yz} \frac{\partial}{\partial y} (- yz)

= e^{- yz} \frac{\partial}{\partial y} (- yz)

\frac{\partial}{\partial y} (- yz) = - z

= x^{2} e^{- yz} (- z)

Simplify

= - e^{- yz} x^{2} z

\int \frac{1}{2 + 5 y ^{2}} d y

x \to \infty lim (x^{6 x})

5 x - 3

ln (x + 9)

\int (4 x^{3} - 9 x^{2} + 7 x + 3 e) e^{- x} d x

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