What is the derivative of (9x^2-6/(x^2)) ?

The derivative of (9x^2-6/(x^2)) is (12)/(x^3)

What is the first derivative of (9x^2-6/(x^2)) ?

The first derivative of (9x^2-6/(x^2)) is (12)/(x^3)

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\frac{d}{d x} (\frac{9 x ^{2} - 6}{x ^{2}})

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

Solution steps

\frac{d}{d x} (\frac{9 x ^{2} - 6}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 9 x ^{2} - 6 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 9 x ^{2} - 6 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (9 x^{2} - 6) = 18 x

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

= \frac{18 x x ^{2} - 2 x ( 9 x ^{2} - 6 )}{( x ^{2} ) ^{2}}

Simplify

\frac{18 x x ^{2} - 2 x ( 9 x ^{2} - 6 )}{( x ^{2} ) ^{2}} : \frac{12}{x ^{3}}

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

\frac{\partial}{\partial x} (\frac{4}{1 + x ^{2}})

\frac{d}{d x} (1 - x y cos (π y))

f (x) = 5^{x} ln (5)

(1 + x^{4})^{\frac{4}{5}}

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

What is the derivative of (9x^2-6/(x^2)) ?
The derivative of (9x^2-6/(x^2)) is (12)/(x^3)
What is the first derivative of (9x^2-6/(x^2)) ?
The first derivative of (9x^2-6/(x^2)) is (12)/(x^3)