What is the derivative of (x^3+1/(x^2)) ?

The derivative of (x^3+1/(x^2)) is (x^3-2)/(x^3)

What is the first derivative of (x^3+1/(x^2)) ?

The first derivative of (x^3+1/(x^2)) is (x^3-2)/(x^3)

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

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

Solution steps

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

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

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

= \frac{3 x ^{2} x ^{2} - 2 x ( x ^{3} + 1 )}{( x ^{2} ) ^{2}}

Simplify

\frac{3 x ^{2} x ^{2} - 2 x ( x ^{3} + 1 )}{( x ^{2} ) ^{2}} : \frac{x ^{3} - 2}{x ^{3}}

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

\int \frac{1}{1 - x} d x

3 x (y^{2} + 1) d x + y (x^{2} + 2) d y = 0

y^{^{'}} = \frac{x - 1}{y - 4}

\frac{\partial}{\partial y} (3 y^{2} + 3 x^{2} - 12 y)

y^{^{'}} = 3 e^{- 2 x}

What is the derivative of (x^3+1/(x^2)) ?
The derivative of (x^3+1/(x^2)) is (x^3-2)/(x^3)
What is the first derivative of (x^3+1/(x^2)) ?
The first derivative of (x^3+1/(x^2)) is (x^3-2)/(x^3)