What is the derivative of (x^2-2/(5x^3+6)) ?

The derivative of (x^2-2/(5x^3+6)) is (-5x^4+30x^2+12x)/((5x^3+6)^2)

What is the first derivative of (x^2-2/(5x^3+6)) ?

The first derivative of (x^2-2/(5x^3+6)) is (-5x^4+30x^2+12x)/((5x^3+6)^2)

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\frac{d}{d x} (\frac{x ^{2} - 2}{5 x ^{3} + 6})

\frac{- 5 x ^{4} + 30 x ^{2} + 12 x}{( 5 x ^{3} + 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 2}{5 x ^{3} + 6})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 2 ) ( 5 x ^{3} + 6 ) - \frac{d}{d x} ( 5 x ^{3} + 6 ) ( x ^{2} - 2 )}{( 5 x ^{3} + 6 ) ^{2}}

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

\frac{d}{d x} (5 x^{3} + 6) = 15 x^{2}

= \frac{2 x ( 5 x ^{3} + 6 ) - 15 x ^{2} ( x ^{2} - 2 )}{( 5 x ^{3} + 6 ) ^{2}}

Expand

2 x (5 x^{3} + 6) - 15 x^{2} (x^{2} - 2) : - 5 x^{4} + 30 x^{2} + 12 x

= \frac{- 5 x ^{4} + 30 x ^{2} + 12 x}{( 5 x ^{3} + 6 ) ^{2}}

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

\int \frac{arcsin ( x )}{1 - x} d x

f (x) = ln (ln (3 x))

\frac{d}{d x} (\frac{x ^{2}}{x + 7})

n = 1 \sum \infty sin (\frac{1}{n})

What is the derivative of (x^2-2/(5x^3+6)) ?
The derivative of (x^2-2/(5x^3+6)) is (-5x^4+30x^2+12x)/((5x^3+6)^2)
What is the first derivative of (x^2-2/(5x^3+6)) ?
The first derivative of (x^2-2/(5x^3+6)) is (-5x^4+30x^2+12x)/((5x^3+6)^2)