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

The derivative of ((4x^5+5))/(x^3) is (8x^5-15)/(x^4)

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

The first derivative of ((4x^5+5))/(x^3) is (8x^5-15)/(x^4)

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derivative of

\frac{( 4 x ^{5} + 5 )}{x ^{3}}

\frac{8 x ^{5} - 15}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (4 x^{5} + 5) = 20 x^{4}

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

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

Simplify

\frac{20 x ^{4} x ^{3} - 3 x ^{2} ( 4 x ^{5} + 5 )}{( x ^{3} ) ^{2}} : \frac{8 x ^{5} - 15}{x ^{4}}

= \frac{8 x ^{5} - 15}{x ^{4}}

x \frac{d y}{d x} + 6 y = 1 - \frac{4}{x}

\int sec^{7} (2 x) tan (2 x) d x

\int \frac{( x + 1 ) ^{4}}{( x ^{2} + 2 x + 2 ) ^{3}} d x

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\frac{d}{d x} ((1 + 5 x^{2}) (x - x^{2}))

What is the derivative of ((4x^5+5))/(x^3) ?
The derivative of ((4x^5+5))/(x^3) is (8x^5-15)/(x^4)
What is the first derivative of ((4x^5+5))/(x^3) ?
The first derivative of ((4x^5+5))/(x^3) is (8x^5-15)/(x^4)