What is the derivative of ((3x^5-7x^2-4)/(x^2)) ?

The derivative of ((3x^5-7x^2-4)/(x^2)) is (9x^5+8)/(x^3)

What is the first derivative of ((3x^5-7x^2-4)/(x^2)) ?

The first derivative of ((3x^5-7x^2-4)/(x^2)) is (9x^5+8)/(x^3)

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\frac{d}{d x} (\frac{( 3 x ^{5} - 7 x ^{2} - 4 )}{x ^{2}})

\frac{9 x ^{5} + 8}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{( 3 x ^{5} - 7 x ^{2} - 4 )}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x ^{5} - 7 x ^{2} - 4 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 3 x ^{5} - 7 x ^{2} - 4 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (3 x^{5} - 7 x^{2} - 4) = 15 x^{4} - 14 x

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

= \frac{( 15 x ^{4} - 14 x ) x ^{2} - 2 x ( 3 x ^{5} - 7 x ^{2} - 4 )}{( x ^{2} ) ^{2}}

Simplify

\frac{( 15 x ^{4} - 14 x ) x ^{2} - 2 x ( 3 x ^{5} - 7 x ^{2} - 4 )}{( x ^{2} ) ^{2}} : \frac{9 x ^{5} + 8}{x ^{3}}

= \frac{9 x ^{5} + 8}{x ^{3}}

\frac{2 x - 1}{2 x + 3}

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

\int_{7}^{9} \frac{y}{y ^{2} - 3 y - 4} d y

\frac{d}{d t} (e^{4 t} sin (t))

f (x) = 3 x^{2} - x^{3}

What is the derivative of ((3x^5-7x^2-4)/(x^2)) ?
The derivative of ((3x^5-7x^2-4)/(x^2)) is (9x^5+8)/(x^3)
What is the first derivative of ((3x^5-7x^2-4)/(x^2)) ?
The first derivative of ((3x^5-7x^2-4)/(x^2)) is (9x^5+8)/(x^3)