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

(\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}

t a y l or (9 - x^{2})^{- \frac{1}{2}}

t an g e n t y = 2 x^{2} + 9 x - 7

\frac{d}{d x} (2 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

f (x) = sec (x)

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