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

The derivative of (5x^4-3x^3/(x^5)) is (-5x+6)/(x^3)

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

The first derivative of (5x^4-3x^3/(x^5)) is (-5x+6)/(x^3)

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

\frac{- 5 x + 6}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x ^{4} - 3 x ^{3} ) x ^{5} - \frac{d}{d x} ( x ^{5} ) ( 5 x ^{4} - 3 x ^{3} )}{( x ^{5} ) ^{2}}

\frac{d}{d x} (5 x^{4} - 3 x^{3}) = 20 x^{3} - 9 x^{2}

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{( 20 x ^{3} - 9 x ^{2} ) x ^{5} - 5 x ^{4} ( 5 x ^{4} - 3 x ^{3} )}{( x ^{5} ) ^{2}}

Simplify

\frac{( 20 x ^{3} - 9 x ^{2} ) x ^{5} - 5 x ^{4} ( 5 x ^{4} - 3 x ^{3} )}{( x ^{5} ) ^{2}} : \frac{- 5 x + 6}{x ^{3}}

= \frac{- 5 x + 6}{x ^{3}}

\int \frac{1}{4} (2 x + 1) d x

\frac{d}{d x} (2 - y - 2 x)

x \to - 2 lim (x (- 2))

f (x) = (\frac{x + 4}{x - 4})^{5}

What is the derivative of (5x^4-3x^3/(x^5)) ?
The derivative of (5x^4-3x^3/(x^5)) is (-5x+6)/(x^3)
What is the first derivative of (5x^4-3x^3/(x^5)) ?
The first derivative of (5x^4-3x^3/(x^5)) is (-5x+6)/(x^3)