What is the derivative of (x^3)/(x^2+12) ?

The derivative of (x^3)/(x^2+12) is (x^4+36x^2)/((x^2+12)^2)

What is the first derivative of (x^3)/(x^2+12) ?

The first derivative of (x^3)/(x^2+12) is (x^4+36x^2)/((x^2+12)^2)

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derivative of

\frac{x ^{3}}{x ^{2} + 12}

\frac{x ^{4} + 36 x ^{2}}{( x ^{2} + 12 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{x ^{2} + 12})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{3} ) ( x ^{2} + 12 ) - \frac{d}{d x} ( x ^{2} + 12 ) x ^{3}}{( x ^{2} + 12 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 12) = 2 x

= \frac{3 x ^{2} ( x ^{2} + 12 ) - 2 x x ^{3}}{( x ^{2} + 12 ) ^{2}}

Simplify

\frac{3 x ^{2} ( x ^{2} + 12 ) - 2 x x ^{3}}{( x ^{2} + 12 ) ^{2}} : \frac{x ^{4} + 36 x ^{2}}{( x ^{2} + 12 ) ^{2}}

= \frac{x ^{4} + 36 x ^{2}}{( x ^{2} + 12 ) ^{2}}

y y^{^{'}} = 8 sin (x)

\frac{d}{d x} (\frac{x}{( x - 8 ) ^{2}})

f (x) = e^{x}, at x = ln (12)

x \to 1 lim (x^{3} - x^{2} + 4 x)

sin (2 x + 3)

What is the derivative of (x^3)/(x^2+12) ?
The derivative of (x^3)/(x^2+12) is (x^4+36x^2)/((x^2+12)^2)
What is the first derivative of (x^3)/(x^2+12) ?
The first derivative of (x^3)/(x^2+12) is (x^4+36x^2)/((x^2+12)^2)