What is the derivative of (x^2+x/(3x-1)) ?

The derivative of (x^2+x/(3x-1)) is (3x^2-2x-1)/((3x-1)^2)

What is the first derivative of (x^2+x/(3x-1)) ?

The first derivative of (x^2+x/(3x-1)) is (3x^2-2x-1)/((3x-1)^2)

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\frac{d}{d x} (\frac{x ^{2} + x}{3 x - 1})

\frac{3 x ^{2} - 2 x - 1}{( 3 x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + x}{3 x - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + x ) ( 3 x - 1 ) - \frac{d}{d x} ( 3 x - 1 ) ( x ^{2} + x )}{( 3 x - 1 ) ^{2}}

\frac{d}{d x} (x^{2} + x) = 2 x + 1

\frac{d}{d x} (3 x - 1) = 3

= \frac{( 2 x + 1 ) ( 3 x - 1 ) - 3 ( x ^{2} + x )}{( 3 x - 1 ) ^{2}}

Expand

(2 x + 1) (3 x - 1) - 3 (x^{2} + x) : 3 x^{2} - 2 x - 1

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

\frac{d}{d x} (\frac{x}{x ^{2} + 7})

sin (k t)

\int - 2 e^{x} x^{3} d x

\frac{1}{x ^{11}}

(y^{3} + 7)^{6}

What is the derivative of (x^2+x/(3x-1)) ?
The derivative of (x^2+x/(3x-1)) is (3x^2-2x-1)/((3x-1)^2)
What is the first derivative of (x^2+x/(3x-1)) ?
The first derivative of (x^2+x/(3x-1)) is (3x^2-2x-1)/((3x-1)^2)