What is the derivative of (2x^2-1/(3x+5)) ?

The derivative of (2x^2-1/(3x+5)) is (6x^2+20x+3)/((3x+5)^2)

What is the first derivative of (2x^2-1/(3x+5)) ?

The first derivative of (2x^2-1/(3x+5)) is (6x^2+20x+3)/((3x+5)^2)

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\frac{d}{d x} (\frac{2 x ^{2} - 1}{3 x + 5})

\frac{6 x ^{2} + 20 x + 3}{( 3 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{2} - 1}{3 x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x ^{2} - 1 ) ( 3 x + 5 ) - \frac{d}{d x} ( 3 x + 5 ) ( 2 x ^{2} - 1 )}{( 3 x + 5 ) ^{2}}

\frac{d}{d x} (2 x^{2} - 1) = 4 x

\frac{d}{d x} (3 x + 5) = 3

= \frac{4 x ( 3 x + 5 ) - 3 ( 2 x ^{2} - 1 )}{( 3 x + 5 ) ^{2}}

Expand

4 x (3 x + 5) - 3 (2 x^{2} - 1) : 6 x^{2} + 20 x + 3

= \frac{6 x ^{2} + 20 x + 3}{( 3 x + 5 ) ^{2}}

What is the derivative of (2x^2-1/(3x+5)) ?
The derivative of (2x^2-1/(3x+5)) is (6x^2+20x+3)/((3x+5)^2)
What is the first derivative of (2x^2-1/(3x+5)) ?
The first derivative of (2x^2-1/(3x+5)) is (6x^2+20x+3)/((3x+5)^2)