What is the derivative of-(12x)/((6x^2+5)^2) ?

The derivative of-(12x)/((6x^2+5)^2) is -(12(5-18x^2))/((6x^2+5)^3)

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

The first derivative of-(12x)/((6x^2+5)^2) is -(12(5-18x^2))/((6x^2+5)^3)

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derivative of

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

- \frac{12 ( 5 - 18 x ^{2} )}{( 6 x ^{2} + 5 ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{12 x}{( 6 x ^{2} + 5 ) ^{2}})

Take the constant out:

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

= - 12 \frac{d}{d x} (\frac{x}{( 6 x ^{2} + 5 ) ^{2}})

Apply the Quotient Rule:

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

= - 12 \cdot \frac{\frac{d x}{d x} ( 6 x ^{2} + 5 ) ^{2} - \frac{d}{d x} ( ( 6 x ^{2} + 5 ) ^{2} ) x}{( ( 6 x ^{2} + 5 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((6 x^{2} + 5)^{2}) = 24 x (6 x^{2} + 5)

= - 12 \cdot \frac{1 \cdot ( 6 x ^{2} + 5 ) ^{2} - 24 x ( 6 x ^{2} + 5 ) x}{( ( 6 x ^{2} + 5 ) ^{2} ) ^{2}}

Simplify

- 12 \cdot \frac{1 \cdot ( 6 x ^{2} + 5 ) ^{2} - 24 x ( 6 x ^{2} + 5 ) x}{( ( 6 x ^{2} + 5 ) ^{2} ) ^{2}} : - \frac{12 ( 5 - 18 x ^{2} )}{( 6 x ^{2} + 5 ) ^{3}}

= - \frac{12 ( 5 - 18 x ^{2} )}{( 6 x ^{2} + 5 ) ^{3}}

\frac{1}{x} + \frac{1}{x ^{3}} - \frac{4}{x}

\frac{d}{d x} (\frac{x}{x ^{2} - x + 25})

\frac{d}{d t} (t^{n} e^{a t})

\int (3 x + 4)^{2} d x

x \to 2 lim (\frac{∣ x - 2 ∣}{2 - x})

What is the derivative of-(12x)/((6x^2+5)^2) ?
The derivative of-(12x)/((6x^2+5)^2) is -(12(5-18x^2))/((6x^2+5)^3)
What is the first derivative of-(12x)/((6x^2+5)^2) ?
The first derivative of-(12x)/((6x^2+5)^2) is -(12(5-18x^2))/((6x^2+5)^3)