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

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

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

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

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derivative of

f (x) = \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}

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

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

\int cos (3 z + 4) d z

n = 1 \sum \infty \frac{1}{n 2 ^{n}}

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