What is the derivative of-(33e^{1/x})/(x^2) ?

The derivative of-(33e^{1/x})/(x^2) is -(33(-e^{1/x}-2e^{1/x}x))/(x^4)

What is the first derivative of-(33e^{1/x})/(x^2) ?

The first derivative of-(33e^{1/x})/(x^2) is -(33(-e^{1/x}-2e^{1/x}x))/(x^4)

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derivative of

- \frac{33 e ^{\frac{1}{x}}}{x ^{2}}

- \frac{33 ( - e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x )}{x ^{4}}

Solution steps

\frac{d}{d x} (- \frac{33 e ^{\frac{1}{x}}}{x ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 33 \frac{d}{d x} (\frac{e ^{\frac{1}{x}}}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - 33 \cdot \frac{\frac{d}{d x} ( e ^{\frac{1}{x}} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) e ^{\frac{1}{x}}}{( x ^{2} ) ^{2}}

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

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

= - 33 \cdot \frac{( - \frac{e ^{\frac{1}{x}}}{x ^{2}} ) x ^{2} - 2 x e ^{\frac{1}{x}}}{( x ^{2} ) ^{2}}

Simplify

- 33 \cdot \frac{( - \frac{e ^{\frac{1}{x}}}{x ^{2}} ) x ^{2} - 2 x e ^{\frac{1}{x}}}{( x ^{2} ) ^{2}} : - \frac{33 ( - e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x )}{x ^{4}}

= - \frac{33 ( - e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x )}{x ^{4}}

n = 0 \sum \infty (- \frac{3}{4})^{n - 1}

\int 2 θ cos (θ) d θ

x \to 0 lim (\frac{2 ^{2 x} - 2 ^{- 2 x}}{2 ^{3 x} - 2 ^{- 3 x}})

\frac{d}{d x} (- \frac{8}{x ^{3}} + \frac{2}{x ^{2}})

What is the derivative of-(33e^{1/x})/(x^2) ?
The derivative of-(33e^{1/x})/(x^2) is -(33(-e^{1/x}-2e^{1/x}x))/(x^4)
What is the first derivative of-(33e^{1/x})/(x^2) ?
The first derivative of-(33e^{1/x})/(x^2) is -(33(-e^{1/x}-2e^{1/x}x))/(x^4)