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

The derivative of (5x/((x^3-6)^2)) is (5(-5x^3-6))/((x^3-6)^3)

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

The first derivative of (5x/((x^3-6)^2)) is (5(-5x^3-6))/((x^3-6)^3)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

= 5 \cdot \frac{1 \cdot ( x ^{3} - 6 ) ^{2} - 6 x ^{2} ( x ^{3} - 6 ) x}{( ( x ^{3} - 6 ) ^{2} ) ^{2}}

Simplify

5 \cdot \frac{1 \cdot ( x ^{3} - 6 ) ^{2} - 6 x ^{2} ( x ^{3} - 6 ) x}{( ( x ^{3} - 6 ) ^{2} ) ^{2}} : \frac{5 ( - 5 x ^{3} - 6 )}{( x ^{3} - 6 ) ^{3}}

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

\frac{\partial}{\partial x} (\frac{3}{2 x ^{2}})

y^{2} y^{^{'}} = x^{2}

\int_{0}^{\frac{π}{3}} x sin (12 x) d x

\int x^{\frac{2}{3}} d x

f (x) = \frac{sin ^{2} ( x )}{x ^{2}}

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