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Popular Calculus >

derivative of (x^3-6/(x^2))

Solution

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

Solution

\frac{x ^{3} + 12}{x ^{3}}

Solution steps

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

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

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

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

Simplify

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

= \frac{x ^{3} + 12}{x ^{3}}

Graph

Popular Examples

integral of 1/(x^{1/2)+x^{1/3}}

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

derivative of arctan(sin(ln(x^3)))

\frac{d}{d x} (arctan (sin (ln (x^{3}))))

integral of ((2x^2-x+3))/(sqrt(x))

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

slope of y=2x^3-x^2+3

s l o p e y = 2 x^{3} - x^{2} + 3

\frac{d y}{d x} = 4 x y

Frequently Asked Questions (FAQ)

What is the derivative of (x^3-6/(x^2)) ?
The derivative of (x^3-6/(x^2)) is (x^3+12)/(x^3)
What is the first derivative of (x^3-6/(x^2)) ?
The first derivative of (x^3-6/(x^2)) is (x^3+12)/(x^3)