What is (\partial)/(\partial x)(y^4e^{-x}) ?

The answer to (\partial)/(\partial x)(y^4e^{-x}) is -e^{-x}y^4

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(\partial)/(\partial x)(y^4e^{-x})

\frac{\partial}{\partial x} (y^{4} e^{- x})

- e^{- x} y^{4}

Solution steps

\frac{\partial}{\partial x} (y^{4} e^{- x})

Treat

y

as a constant

Take the constant out:

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

= y^{4} \frac{\partial}{\partial x} (e^{- x})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- x) = - 1

= y^{4} e^{- x} (- 1)

Simplify

= - e^{- x} y^{4}

\int x^{2} (x^{3} - 2)^{4} d x

\int \frac{( ln ( x ^{5} ) )}{x} d x

\frac{\partial}{\partial y} (7 x^{2} e^{y})

f (x) = x^{3} x^{4} + 3 x^{2} - 2

e^{x}, e^{- x}, 0, 1

What is (\partial)/(\partial x)(y^4e^{-x}) ?
The answer to (\partial)/(\partial x)(y^4e^{-x}) is -e^{-x}y^4