What is the derivative of-(6x/(6x^2+8)) ?

The derivative of-(6x/(6x^2+8)) is -(3(-3x^2+4))/((3x^2+4)^2)

What is the first derivative of-(6x/(6x^2+8)) ?

The first derivative of-(6x/(6x^2+8)) is -(3(-3x^2+4))/((3x^2+4)^2)

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\frac{d}{d x} (- \frac{6 x}{6 x ^{2} + 8})

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

Solution steps

\frac{d}{d x} (- \frac{6 x}{6 x ^{2} + 8})

Simplify

- \frac{6 x}{6 x ^{2} + 8} : - \frac{3 x}{3 x ^{2} + 4}

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

= - 3 \cdot \frac{\frac{d x}{d x} ( 3 x ^{2} + 4 ) - \frac{d}{d x} ( 3 x ^{2} + 4 ) x}{( 3 x ^{2} + 4 ) ^{2}}

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

\frac{d}{d x} (3 x^{2} + 4) = 6 x

= - 3 \cdot \frac{1 \cdot ( 3 x ^{2} + 4 ) - 6 xx}{( 3 x ^{2} + 4 ) ^{2}}

Simplify

- 3 \cdot \frac{1 \cdot ( 3 x ^{2} + 4 ) - 6 xx}{( 3 x ^{2} + 4 ) ^{2}} : - \frac{3 ( - 3 x ^{2} + 4 )}{( 3 x ^{2} + 4 ) ^{2}}

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

\int_{- 3}^{2} π (y^{2} + 2 y + 4)^{2} d y

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

\int t csc^{2} (t) d t

\int 6 x e^{- x} d x

\int \frac{1}{sin ( x ) cos ^{5} ( x )} d x

What is the derivative of-(6x/(6x^2+8)) ?
The derivative of-(6x/(6x^2+8)) is -(3(-3x^2+4))/((3x^2+4)^2)
What is the first derivative of-(6x/(6x^2+8)) ?
The first derivative of-(6x/(6x^2+8)) is -(3(-3x^2+4))/((3x^2+4)^2)