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

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

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

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

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\frac{d}{d x} (e^{\frac{1}{f ( x )}})

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

Solution steps

\frac{d}{d x} (e^{\frac{1}{f ( x )}})

Apply the chain rule:

e^{\frac{1}{f ( x )}} \frac{d}{d x} (\frac{1}{f ( x )})

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

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

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

Simplify

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

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

\int \frac{1}{5 ^{x}} d x

\frac{d y}{d x} + 2 x y = 2 x

\frac{1}{s ^{2} - 3 s + 5}

y^{^{'}} = \frac{( 4 t ^{3} + 1 )}{( 2 y - 6 )}

x \to - 1 lim (\frac{2 x}{∣ x ∣})

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