What is the derivative of (9x^2+3)/x ?

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

What is the first derivative of (9x^2+3)/x ?

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

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derivative of

\frac{9 x ^{2} + 3}{x}

\frac{9 x ^{2} - 3}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{9 x ^{2} + 3}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 9 x ^{2} + 3 ) x - \frac{d x}{d x} ( 9 x ^{2} + 3 )}{x ^{2}}

\frac{d}{d x} (9 x^{2} + 3) = 18 x

\frac{d x}{d x} = 1

= \frac{18 xx - 1 \cdot ( 9 x ^{2} + 3 )}{x ^{2}}

Simplify

\frac{18 xx - 1 \cdot ( 9 x ^{2} + 3 )}{x ^{2}} : \frac{9 x ^{2} - 3}{x ^{2}}

= \frac{9 x ^{2} - 3}{x ^{2}}

sin (π t)

y = x + \frac{1}{x}

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

y^{^{'}} + y = e^{- 4 t} cos (3 t), y (0) = 0

x^{2} y^{^{'}} + x y = 3

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