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

The derivative of ((2x^5+3x^4-x^3+2)/(x^2)) is (6x^5+6x^4-x^3-4)/(x^3)

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

The first derivative of ((2x^5+3x^4-x^3+2)/(x^2)) is (6x^5+6x^4-x^3-4)/(x^3)

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

\frac{6 x ^{5} + 6 x ^{4} - x ^{3} - 4}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (2 x^{5} + 3 x^{4} - x^{3} + 2) = 10 x^{4} + 12 x^{3} - 3 x^{2}

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

= \frac{( 10 x ^{4} + 12 x ^{3} - 3 x ^{2} ) x ^{2} - 2 x ( 2 x ^{5} + 3 x ^{4} - x ^{3} + 2 )}{( x ^{2} ) ^{2}}

Simplify

\frac{( 10 x ^{4} + 12 x ^{3} - 3 x ^{2} ) x ^{2} - 2 x ( 2 x ^{5} + 3 x ^{4} - x ^{3} + 2 )}{( x ^{2} ) ^{2}} : \frac{6 x ^{5} + 6 x ^{4} - x ^{3} - 4}{x ^{3}}

= \frac{6 x ^{5} + 6 x ^{4} - x ^{3} - 4}{x ^{3}}

12 x^{2} - 12 x - 2

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

\frac{d}{d x} (ln (x^{2} - 9))

\int 6 x ln (3 x) d x

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

What is the derivative of ((2x^5+3x^4-x^3+2)/(x^2)) ?
The derivative of ((2x^5+3x^4-x^3+2)/(x^2)) is (6x^5+6x^4-x^3-4)/(x^3)
What is the first derivative of ((2x^5+3x^4-x^3+2)/(x^2)) ?
The first derivative of ((2x^5+3x^4-x^3+2)/(x^2)) is (6x^5+6x^4-x^3-4)/(x^3)