What is the derivative of (5x^2+e^x/(x^3)) ?

The derivative of (5x^2+e^x/(x^3)) is (-5x^2+e^xx-3e^x)/(x^4)

What is the first derivative of (5x^2+e^x/(x^3)) ?

The first derivative of (5x^2+e^x/(x^3)) is (-5x^2+e^xx-3e^x)/(x^4)

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\frac{d}{d x} (\frac{5 x ^{2} + e ^{x}}{x ^{3}})

\frac{- 5 x ^{2} + e ^{x} x - 3 e ^{x}}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{5 x ^{2} + 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} ( 5 x ^{2} + e ^{x} ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 5 x ^{2} + e ^{x} )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (5 x^{2} + e^{x}) = 10 x + e^{x}

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

= \frac{( 10 x + e ^{x} ) x ^{3} - 3 x ^{2} ( 5 x ^{2} + e ^{x} )}{( x ^{3} ) ^{2}}

Simplify

\frac{( 10 x + e ^{x} ) x ^{3} - 3 x ^{2} ( 5 x ^{2} + e ^{x} )}{( x ^{3} ) ^{2}} : \frac{- 5 x ^{2} + e ^{x} x - 3 e ^{x}}{x ^{4}}

= \frac{- 5 x ^{2} + e ^{x} x - 3 e ^{x}}{x ^{4}}

\frac{d}{d x} (\frac{1}{1 - 4 x})

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

x \to - 5 lim (f (x))

\int 2 x^{5} d x

\int_{0}^{x} (2 t^{2} + t) d t

What is the derivative of (5x^2+e^x/(x^3)) ?
The derivative of (5x^2+e^x/(x^3)) is (-5x^2+e^xx-3e^x)/(x^4)
What is the first derivative of (5x^2+e^x/(x^3)) ?
The first derivative of (5x^2+e^x/(x^3)) is (-5x^2+e^xx-3e^x)/(x^4)