What is (\partial)/(\partial x)(e^{-x^4-y^3}) ?

The answer to (\partial)/(\partial x)(e^{-x^4-y^3}) is -4e^{-x^4-y^3}x^3

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(\partial)/(\partial x)(e^{-x^4-y^3})

\frac{\partial}{\partial x} (e^{- x^{4} - y^{3}})

- 4 e^{- x^{4} - y^{3}} x^{3}

Solution steps

\frac{\partial}{\partial x} (e^{- x^{4} - y^{3}})

Treat

y

as a constant

Apply the chain rule:

e^{- x^{4} - y^{3}} \frac{\partial}{\partial x} (- x^{4} - y^{3})

= e^{- x^{4} - y^{3}} \frac{\partial}{\partial x} (- x^{4} - y^{3})

\frac{\partial}{\partial x} (- x^{4} - y^{3}) = - 4 x^{3}

= e^{- x^{4} - y^{3}} (- 4 x^{3})

Simplify

= - 4 e^{- x^{4} - y^{3}} x^{3}

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

\frac{d}{d x} (2 x + 3 x^{2})

\frac{d ^{2}}{d x ^{2}} (ln (2 x + 4))

y = x^{2}, y = 20 - x

\int csc^{2} (\frac{x}{6}) d x

What is (\partial)/(\partial x)(e^{-x^4-y^3}) ?
The answer to (\partial)/(\partial x)(e^{-x^4-y^3}) is -4e^{-x^4-y^3}x^3