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

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

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

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

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

\frac{x ^{3} - 2 x - 6}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( 3 x ^{2} + 2 ) x ^{2} - 2 x ( x ^{3} + 2 x + 3 )}{( x ^{2} ) ^{2}} : \frac{x ^{3} - 2 x - 6}{x ^{3}}

= \frac{x ^{3} - 2 x - 6}{x ^{3}}

\int \frac{y}{16 + y ^{2}} d y

x^{5} + y^{4} x^{6} + 4 y^{^{'}} = 0

\frac{\partial}{\partial x} (- 6 e^{x} cos (yz))

x \to 1 lim (\frac{x ^{4} - 6 x ^{2} + 8 x - 3}{x ^{4} - 2 x ^{3} + 2 x - 1})

\int_{0}^{2} 2 π (9 - x) (8 - x^{3}) d x

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