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

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

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

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

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

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

Solution steps

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

\frac{d}{d x} (2 x^{3} - 1) = 6 x^{2}

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

= \frac{6 x ^{2} x ^{2} - 2 x ( 2 x ^{3} - 1 )}{( x ^{2} ) ^{2}}

Simplify

\frac{6 x ^{2} x ^{2} - 2 x ( 2 x ^{3} - 1 )}{( x ^{2} ) ^{2}} : \frac{2 ( x ^{3} + 1 )}{x ^{3}}

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

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

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

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

sin (\frac{2 t}{3})

934 + 20 x - 0.079 x^{2}

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