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

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

Popular >

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

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the chain rule:

e^{- x z} \frac{\partial}{\partial z} (- x z)

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

\frac{\partial}{\partial z} (- x z) = - x

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

Simplify

x y^{2} e^{- x z} (- x) : - e^{- x z} x^{2} y^{2}

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

(12 x^{2} - 20 y^{2}) d x + (- 20 x y + 36 x^{- 1} y^{3}) d y = 0

\int e^{x} d x

\int \frac{x ^{2}}{x + 2} d x

y = 5 x^{3} + 4 x^{2} - 6, (1, 3)

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

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