What is (\partial)/(\partial x)(e^{-(x^7+y^7)}) ?

The answer to (\partial)/(\partial x)(e^{-(x^7+y^7)}) is -7e^{-x^7-y^7}x^6

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(\partial)/(\partial x)(e^{-(x^7+y^7)})

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

- 7 e^{- x^{7} - y^{7}} x^{6}

Solution steps

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

Simplify

e^{- (x^{7} + y^{7})} : e^{- x^{7} - y^{7}}

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- x^{7} - y^{7}) = - 7 x^{6}

= e^{- x^{7} - y^{7}} (- 7 x^{6})

Simplify

= - 7 e^{- x^{7} - y^{7}} x^{6}

\frac{d y}{d x} = e^{x + y} + x^{2} e^{y}

x \to \infty lim (e^{7 x})

(9 - x^{2})^{- \frac{1}{2}}

y = 2 x^{2} + 9 x - 7

\frac{\partial}{\partial x} (x^{8} y^{9} - x^{7} y^{8})

What is (\partial)/(\partial x)(e^{-(x^7+y^7)}) ?
The answer to (\partial)/(\partial x)(e^{-(x^7+y^7)}) is -7e^{-x^7-y^7}x^6