What is the derivative of f(x)=(4x^2-7x+5)/(2x+3) ?

The derivative of f(x)=(4x^2-7x+5)/(2x+3) is (8x^2+24x-31)/((2x+3)^2)

What is the first derivative of f(x)=(4x^2-7x+5)/(2x+3) ?

The first derivative of f(x)=(4x^2-7x+5)/(2x+3) is (8x^2+24x-31)/((2x+3)^2)

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derivative of

f (x) = \frac{4 x ^{2} - 7 x + 5}{2 x + 3}

\frac{8 x ^{2} + 24 x - 31}{( 2 x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{2} - 7 x + 5}{2 x + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} - 7 x + 5 ) ( 2 x + 3 ) - \frac{d}{d x} ( 2 x + 3 ) ( 4 x ^{2} - 7 x + 5 )}{( 2 x + 3 ) ^{2}}

\frac{d}{d x} (4 x^{2} - 7 x + 5) = 8 x - 7

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

= \frac{( 8 x - 7 ) ( 2 x + 3 ) - 2 ( 4 x ^{2} - 7 x + 5 )}{( 2 x + 3 ) ^{2}}

Expand

(8 x - 7) (2 x + 3) - 2 (4 x^{2} - 7 x + 5) : 8 x^{2} + 24 x - 31

= \frac{8 x ^{2} + 24 x - 31}{( 2 x + 3 ) ^{2}}

f (x) = 15 e^{x^{2}}

f (x) = 3 x^{2} + 12

\frac{d}{d x} (\frac{1}{x + \frac{1}{x + 1}})

\frac{\partial}{\partial x} (ln (sin (x y)))

sin^{2} (4 t)

What is the derivative of f(x)=(4x^2-7x+5)/(2x+3) ?
The derivative of f(x)=(4x^2-7x+5)/(2x+3) is (8x^2+24x-31)/((2x+3)^2)
What is the first derivative of f(x)=(4x^2-7x+5)/(2x+3) ?
The first derivative of f(x)=(4x^2-7x+5)/(2x+3) is (8x^2+24x-31)/((2x+3)^2)