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

The derivative of (2x^3/(sqrt(x^2-3))) is (2(2x^4-9x^2))/((x^2-3)sqrt(x^2-3))

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

The first derivative of (2x^3/(sqrt(x^2-3))) is (2(2x^4-9x^2))/((x^2-3)sqrt(x^2-3))

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

\frac{2 ( 2 x ^{4} - 9 x ^{2} )}{( x ^{2} - 3 ) x ^{2} - 3}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

2 \cdot \frac{3 x ^{2} x ^{2} - 3 - \frac{x}{x ^{2} - 3} x ^{3}}{( x ^{2} - 3 ) ^{2}} : \frac{2 ( 2 x ^{4} - 9 x ^{2} )}{( x ^{2} - 3 ) x ^{2} - 3}

= \frac{2 ( 2 x ^{4} - 9 x ^{2} )}{( x ^{2} - 3 ) x ^{2} - 3}

What is the derivative of (2x^3/(sqrt(x^2-3))) ?
The derivative of (2x^3/(sqrt(x^2-3))) is (2(2x^4-9x^2))/((x^2-3)sqrt(x^2-3))
What is the first derivative of (2x^3/(sqrt(x^2-3))) ?
The first derivative of (2x^3/(sqrt(x^2-3))) is (2(2x^4-9x^2))/((x^2-3)sqrt(x^2-3))