What is the derivative of r(2x)/(3x^2-4) ?

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

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

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

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derivative of

r \frac{2 x}{3 x ^{2} - 4}

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

Solution steps

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

Take the constant out:

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

= r \cdot 2 \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}}

= r \cdot 2 \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

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

Simplify

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

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

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

(x^{2} - 2 x)^{3}

in (x^{2})

\int_{0}^{c} 10 e^{2 x} d x

\int (\frac{3}{x ^{3}}) d x

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