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

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

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

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

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derivative of

\frac{x ^{2} + 1}{2 x - 3}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x^{2} = \frac{4 x + y}{4 x - y}

\int \frac{2 x}{4 - x ^{4}} d x

\int \frac{x + 4}{x ^{3}} d x

f (x) = 2 x - 1

\int (4 x^{7} - 3 cos (x)) d x

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