What is the derivative of e^{1/(x^2}+1/(e^{x^2)}) ?

The derivative of e^{1/(x^2}+1/(e^{x^2)}) is -(2e^{1/(x^2)})/(x^3)-2e^{-x^2}x

What is the first derivative of e^{1/(x^2}+1/(e^{x^2)}) ?

The first derivative of e^{1/(x^2}+1/(e^{x^2)}) is -(2e^{1/(x^2)})/(x^3)-2e^{-x^2}x

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\frac{d}{d x} (e^{\frac{1}{x ^{2}}} + \frac{1}{e ^{x^{2}}})

- \frac{2 e ^{\frac{1}{x ^{2}}}}{x ^{3}} - 2 e^{- x^{2}} x

Solution steps

\frac{d}{d x} (e^{\frac{1}{x ^{2}}} + \frac{1}{e ^{x^{2}}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{\frac{1}{x ^{2}}}) + \frac{d}{d x} (\frac{1}{e ^{x^{2}}})

\frac{d}{d x} (e^{\frac{1}{x ^{2}}}) = - \frac{2 e ^{\frac{1}{x ^{2}}}}{x ^{3}}

\frac{d}{d x} (\frac{1}{e ^{x^{2}}}) = - 2 e^{- x^{2}} x

= - \frac{2 e ^{\frac{1}{x ^{2}}}}{x ^{3}} - 2 e^{- x^{2}} x

\int \frac{x ^{2}}{4} - 4 x + 17 d x

\frac{d}{d x} (in (x + 3))

\frac{( x ^{2} + 2 y ^{2} ) d x}{d y} = x y

\int_{5}^{8} \frac{y}{y ^{2} - y - 2} d y

e^{x}, e^{5 x}, 0, 1

What is the derivative of e^{1/(x^2}+1/(e^{x^2)}) ?
The derivative of e^{1/(x^2}+1/(e^{x^2)}) is -(2e^{1/(x^2)})/(x^3)-2e^{-x^2}x
What is the first derivative of e^{1/(x^2}+1/(e^{x^2)}) ?
The first derivative of e^{1/(x^2}+1/(e^{x^2)}) is -(2e^{1/(x^2)})/(x^3)-2e^{-x^2}x