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

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

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

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

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derivative of

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

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

Solution steps

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

Treat

x

as a constant

Apply the Quotient Rule:

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

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

\frac{d y}{d y} = 1

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

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

1 \cdot (3 y^{2} - x) - 6 yy = - 3 y^{2} - x

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

\frac{x}{( x ^{2} + a ^{2} )}

\frac{1 - 1}{x}

3 ln (6 x + 1)

\frac{2 x ^{2}}{( x ^{2} + y ^{2} )}

(x + 2)^{2} \cdot (x - 3)^{3}

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