What is the derivative of (e^x/(7x^3)) ?

The derivative of (e^x/(7x^3)) is (e^x(x-3))/(7x^4)

What is the first derivative of (e^x/(7x^3)) ?

The first derivative of (e^x/(7x^3)) is (e^x(x-3))/(7x^4)

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\frac{d}{d x} (\frac{e ^{x}}{7 x ^{3}})

\frac{e ^{x} ( x - 3 )}{7 x ^{4}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{3}})

Take the constant out:

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

= \frac{1}{7} \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}{7} \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}{7} \cdot \frac{e ^{x} x ^{3} - 3 x ^{2} e ^{x}}{( x ^{3} ) ^{2}}

Simplify

\frac{1}{7} \cdot \frac{e ^{x} x ^{3} - 3 x ^{2} e ^{x}}{( x ^{3} ) ^{2}} : \frac{e ^{x} ( x - 3 )}{7 x ^{4}}

= \frac{e ^{x} ( x - 3 )}{7 x ^{4}}

\int \frac{sin ( x )}{cos ( x ) - cos ^{2} ( x )} d x

\frac{d y}{d x} = \frac{( 1 - y )}{1 - x}

\int 4 cos (2 θ - 5) d θ

\int x + ln (x) d x

x \to 0 + lim (- x + 1)

What is the derivative of (e^x/(7x^3)) ?
The derivative of (e^x/(7x^3)) is (e^x(x-3))/(7x^4)
What is the first derivative of (e^x/(7x^3)) ?
The first derivative of (e^x/(7x^3)) is (e^x(x-3))/(7x^4)