What is the derivative of (e^x/(3x^2)) ?

The derivative of (e^x/(3x^2)) is (e^x(x-2))/(3x^3)

What is the first derivative of (e^x/(3x^2)) ?

The first derivative of (e^x/(3x^2)) is (e^x(x-2))/(3x^3)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1}{3} \cdot \frac{e ^{x} x ^{2} - 2 x e ^{x}}{( x ^{2} ) ^{2}} : \frac{e ^{x} ( x - 2 )}{3 x ^{3}}

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

x \to 0 lim (6 x^{2} (cot (3 x)) (csc (2 x)))

\int_{0}^{1} (x - x^{2})^{2} d x

\int \frac{x - 1}{x ^{2} - 4 x + 3} d x

f (x) = - 2 x^{2}

n = 0 \sum \infty \frac{n}{n + 1} x^{n}

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