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

The answer to (\partial)/(\partial x)(e^{x^{2-y^2}}) is e^{x^{2-y^2}}x^{-y^2+1}(2-y^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(e^{x^{2-y^2}})

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

e^{x^{2 - y^{2}}} x^{- y^{2} + 1} (2 - y^{2})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{x^{2 - y^{2}}} x^{- y^{2} + 1} (2 - y^{2})

\int_{0}^{\frac{π}{2}} cos^{3} (21 x) d x

t \to 0 lim (\frac{e ^{2 t} - 1}{t})

y = ln (30) + 3 0^{x + 4}

x \to 4 lim (x^{2} - 16)

What is (\partial)/(\partial x)(e^{x^{2-y^2}}) ?
The answer to (\partial)/(\partial x)(e^{x^{2-y^2}}) is e^{x^{2-y^2}}x^{-y^2+1}(2-y^2)