What is the derivative of (5x-1/((6x^2-2)^2)) ?

The derivative of (5x-1/((6x^2-2)^2)) is (-45x^2+12x-5)/(4(3x^2-1)^3)

What is the first derivative of (5x-1/((6x^2-2)^2)) ?

The first derivative of (5x-1/((6x^2-2)^2)) is (-45x^2+12x-5)/(4(3x^2-1)^3)

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\frac{d}{d x} (\frac{5 x - 1}{( 6 x ^{2} - 2 ) ^{2}})

\frac{- 45 x ^{2} + 12 x - 5}{4 ( 3 x ^{2} - 1 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{5 x - 1}{( 6 x ^{2} - 2 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x - 1 ) ( 6 x ^{2} - 2 ) ^{2} - \frac{d}{d x} ( ( 6 x ^{2} - 2 ) ^{2} ) ( 5 x - 1 )}{( ( 6 x ^{2} - 2 ) ^{2} ) ^{2}}

\frac{d}{d x} (5 x - 1) = 5

\frac{d}{d x} ((6 x^{2} - 2)^{2}) = 24 x (6 x^{2} - 2)

= \frac{5 ( 6 x ^{2} - 2 ) ^{2} - 24 x ( 6 x ^{2} - 2 ) ( 5 x - 1 )}{( ( 6 x ^{2} - 2 ) ^{2} ) ^{2}}

Simplify

\frac{5 ( 6 x ^{2} - 2 ) ^{2} - 24 x ( 6 x ^{2} - 2 ) ( 5 x - 1 )}{( ( 6 x ^{2} - 2 ) ^{2} ) ^{2}} : \frac{- 45 x ^{2} + 12 x - 5}{4 ( 3 x ^{2} - 1 ) ^{3}}

= \frac{- 45 x ^{2} + 12 x - 5}{4 ( 3 x ^{2} - 1 ) ^{3}}

\frac{d}{d x} (ln (\frac{x}{4}) \cdot (x - 4))

\frac{d}{d x} (\frac{1}{2} (1 - cos (2 x)))

\int \frac{16}{x ^{2} - 4} d x

- 10 x + 11, x^{2} - 5 x - 13

y = \frac{5 x}{( x + 1 ) ^{2}}, (0, 0)

What is the derivative of (5x-1/((6x^2-2)^2)) ?
The derivative of (5x-1/((6x^2-2)^2)) is (-45x^2+12x-5)/(4(3x^2-1)^3)
What is the first derivative of (5x-1/((6x^2-2)^2)) ?
The first derivative of (5x-1/((6x^2-2)^2)) is (-45x^2+12x-5)/(4(3x^2-1)^3)