What is the derivative of (e^x/(5x^3)) ?

The derivative of (e^x/(5x^3)) is (e^x(x-3))/(5x^4)

What is the first derivative of (e^x/(5x^3)) ?

The first derivative of (e^x/(5x^3)) is (e^x(x-3))/(5x^4)

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\frac{d}{d x} (\frac{e ^{x}}{5 x ^{3}})

\frac{e ^{x} ( x - 3 )}{5 x ^{4}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{3}})

Take the constant out:

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

= \frac{1}{5} \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{1}{5} \cdot \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{1}{5} \cdot \frac{e ^{x} x ^{3} - 3 x ^{2} e ^{x}}{( x ^{3} ) ^{2}}

Simplify

\frac{1}{5} \cdot \frac{e ^{x} x ^{3} - 3 x ^{2} e ^{x}}{( x ^{3} ) ^{2}} : \frac{e ^{x} ( x - 3 )}{5 x ^{4}}

= \frac{e ^{x} ( x - 3 )}{5 x ^{4}}

f (x) = (1 + 5 x)^{12}, (0, 1)

10 y^{^{'}} = 10 \cdot 9.81 - 5 y

y = \frac{1}{x - 1}, at x = 6

y^{^{''}} - 4 y^{^{'}} + 3 y = 0

\frac{d}{d x} (- 10 sin (2 x + 10))

What is the derivative of (e^x/(5x^3)) ?
The derivative of (e^x/(5x^3)) is (e^x(x-3))/(5x^4)
What is the first derivative of (e^x/(5x^3)) ?
The first derivative of (e^x/(5x^3)) is (e^x(x-3))/(5x^4)