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Popular >

derivative of (e^x/(x^3))

Solution

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

Solution

\frac{e ^{x} ( x - 3 )}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{e ^{x} x ^{3} - 3 x ^{2} e ^{x}}{( x ^{3} ) ^{2}} : \frac{e ^{x} ( x - 3 )}{x ^{4}}

= \frac{e ^{x} ( x - 3 )}{x ^{4}}

Popular Examples

(\partial)/(\partial y)(-2xe^{xy})

\frac{\partial}{\partial y} (- 2 x e^{x y})

y^{^{'}} = (x - 14)^{2}

y^{''}+324y=sec(18x),y(0)=2,y^'(0)=-1

y^{^{''}} + 324 y = sec (18 x), y (0) = 2, y^{^{'}} (0) = - 1

sum from n=3 to infinity of 3/(n^2-3n+2)

n = 3 \sum \infty \frac{3}{n ^{2} - 3 n + 2}

limit as x approaches 0 of ((1+x)^2)/x

x \to 0 lim (\frac{( 1 + x ) ^{2}}{x})

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(x^3)) ?
The derivative of (e^x/(x^3)) is (e^x(x-3))/(x^4)
What is the first derivative of (e^x/(x^3)) ?
The first derivative of (e^x/(x^3)) is (e^x(x-3))/(x^4)