What is (\partial)/(\partial x)(e^{-x^8-y^4}) ?

The answer to (\partial)/(\partial x)(e^{-x^8-y^4}) is -8e^{-x^8-y^4}x^7

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(\partial)/(\partial x)(e^{-x^8-y^4})

\frac{\partial}{\partial x} (e^{- x^{8} - y^{4}})

- 8 e^{- x^{8} - y^{4}} x^{7}

Solution steps

\frac{\partial}{\partial x} (e^{- x^{8} - y^{4}})

Treat

y

as a constant

Apply the chain rule:

e^{- x^{8} - y^{4}} \frac{\partial}{\partial x} (- x^{8} - y^{4})

= e^{- x^{8} - y^{4}} \frac{\partial}{\partial x} (- x^{8} - y^{4})

\frac{\partial}{\partial x} (- x^{8} - y^{4}) = - 8 x^{7}

= e^{- x^{8} - y^{4}} (- 8 x^{7})

Simplify

= - 8 e^{- x^{8} - y^{4}} x^{7}

\int 6 sin^{3} (6 x) cos^{3} (6 x) d x

x \to \infty + lim (3 e^{x})

\int 7 cos^{3} (4 x) d x

t^{2} y^{^{'}} + y = sin (t), y (1) = 0

\frac{\partial}{\partial y} ((1 - x y)^{- 2})

What is (\partial)/(\partial x)(e^{-x^8-y^4}) ?
The answer to (\partial)/(\partial x)(e^{-x^8-y^4}) is -8e^{-x^8-y^4}x^7