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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

5^{t}

f (x) = sin (x^{5})

\frac{d}{d x} (\frac{- 5}{x ^{2}})

\int \frac{2 x - 4}{( x ^{2} - 4 x + 20 ) ^{2}} d x

\int x^{2} a x^{3} - b d x

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