What is the derivative of e^{9/x} ?

The derivative of e^{9/x} is -(9e^{9/x})/(x^2)

What is the first derivative of e^{9/x} ?

The first derivative of e^{9/x} is -(9e^{9/x})/(x^2)

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\frac{d}{d x} (e^{\frac{9}{x}})

- \frac{9 e ^{\frac{9}{x}}}{x ^{2}}

Solution steps

\frac{d}{d x} (e^{\frac{9}{x}})

Apply the chain rule:

e^{\frac{9}{x}} \frac{d}{d x} (\frac{9}{x})

= e^{\frac{9}{x}} \frac{d}{d x} (\frac{9}{x})

\frac{d}{d x} (\frac{9}{x}) = - \frac{9}{x ^{2}}

= e^{\frac{9}{x}} (- \frac{9}{x ^{2}})

Simplify

e^{\frac{9}{x}} (- \frac{9}{x ^{2}}) : - \frac{9 e ^{\frac{9}{x}}}{x ^{2}}

= - \frac{9 e ^{\frac{9}{x}}}{x ^{2}}

\int \frac{1}{( 5 x ^{2} + x )} d x

\frac{d y}{d x} = 2 cos (5 x)

f (x) = 4 x + 5

x \to 2 + lim (\frac{∣ x - 2 ∣}{x - 2})

What is the derivative of e^{9/x} ?
The derivative of e^{9/x} is -(9e^{9/x})/(x^2)
What is the first derivative of e^{9/x} ?
The first derivative of e^{9/x} is -(9e^{9/x})/(x^2)