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

The derivative of (3x^2+2x/(4x-3)) is (12x^2-18x-6)/((4x-3)^2)

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

The first derivative of (3x^2+2x/(4x-3)) is (12x^2-18x-6)/((4x-3)^2)

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

\frac{12 x ^{2} - 18 x - 6}{( 4 x - 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

(6 x + 2) (4 x - 3) - 4 (3 x^{2} + 2 x) : 12 x^{2} - 18 x - 6

= \frac{12 x ^{2} - 18 x - 6}{( 4 x - 3 ) ^{2}}

g (x) = 3 e^{x} x

\frac{d}{d x} (cos (x) + x cos (y) - y)

\frac{\partial}{\partial x} (x yz + 9 x + 8 y - 4 z)

f (t) = 1

\frac{s}{( s + 1 ) ^{5}}

What is the derivative of (3x^2+2x/(4x-3)) ?
The derivative of (3x^2+2x/(4x-3)) is (12x^2-18x-6)/((4x-3)^2)
What is the first derivative of (3x^2+2x/(4x-3)) ?
The first derivative of (3x^2+2x/(4x-3)) is (12x^2-18x-6)/((4x-3)^2)