What is (\partial)/(\partial x)(e^{-x^3-y^6}) ?

The answer to (\partial)/(\partial x)(e^{-x^3-y^6}) is -3e^{-x^3-y^6}x^2

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(\partial)/(\partial x)(e^{-x^3-y^6})

\frac{\partial}{\partial x} (e^{- x^{3} - y^{6}})

- 3 e^{- x^{3} - y^{6}} x^{2}

Solution steps

\frac{\partial}{\partial x} (e^{- x^{3} - y^{6}})

Treat

y

as a constant

Apply the chain rule:

e^{- x^{3} - y^{6}} \frac{\partial}{\partial x} (- x^{3} - y^{6})

= e^{- x^{3} - y^{6}} \frac{\partial}{\partial x} (- x^{3} - y^{6})

\frac{\partial}{\partial x} (- x^{3} - y^{6}) = - 3 x^{2}

= e^{- x^{3} - y^{6}} (- 3 x^{2})

Simplify

= - 3 e^{- x^{3} - y^{6}} x^{2}

\frac{d}{d x} (- x^{2} + y^{2} - 10)

\int sin^{3} (x) cos (y) d x

\int \frac{1}{1 + u} d u

y = x ln (x) cos (x)

\int \frac{3 x ^{3} + 5 x}{x ^{2} - x - 2} d x

What is (\partial)/(\partial x)(e^{-x^3-y^6}) ?
The answer to (\partial)/(\partial x)(e^{-x^3-y^6}) is -3e^{-x^3-y^6}x^2