What is (\partial)/(\partial x)(e^{-x^5-y^3}) ?

The answer to (\partial)/(\partial x)(e^{-x^5-y^3}) is -5e^{-x^5-y^3}x^4

Popular >

(\partial)/(\partial x)(e^{-x^5-y^3})

\frac{\partial}{\partial x} (e^{- x^{5} - y^{3}})

- 5 e^{- x^{5} - y^{3}} x^{4}

Solution steps

\frac{\partial}{\partial x} (e^{- x^{5} - y^{3}})

Treat

y

as a constant

Apply the chain rule:

e^{- x^{5} - y^{3}} \frac{\partial}{\partial x} (- x^{5} - y^{3})

= e^{- x^{5} - y^{3}} \frac{\partial}{\partial x} (- x^{5} - y^{3})

\frac{\partial}{\partial x} (- x^{5} - y^{3}) = - 5 x^{4}

= e^{- x^{5} - y^{3}} (- 5 x^{4})

Simplify

= - 5 e^{- x^{5} - y^{3}} x^{4}

y + 2 y^{^{'}} + 5 y = 4 \cdot e^{- t} \cdot cos (2 t)

\frac{x - 2}{x - 2}

u \to 2 + lim (u^{2})

\frac{d ^{2} y}{d x ^{2}}

\frac{\partial}{\partial x} (2 x e^{a y} a + 3 e^{x b})

What is (\partial)/(\partial x)(e^{-x^5-y^3}) ?
The answer to (\partial)/(\partial x)(e^{-x^5-y^3}) is -5e^{-x^5-y^3}x^4