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

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

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\frac{d}{d x} (\frac{- x ^{2} + 2}{( x ^{2} + 2 ) ^{2}})

5 \cdot i (t)

\frac{x ^{\frac{1}{3}} - 4}{x ^{\frac{7}{2}}}

y^{^{''}} + 10 y^{^{'}} + 25 y = - 50 e^{- 5 x}

\int \frac{e ^{x}}{( e ^{x} - 5 ) ( e ^{x} - 11 )} d x

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