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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

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

\frac{d}{d x} (\frac{3}{2 x ^{2}})

ln (x) \frac{d y}{d x} + \frac{y}{x} = x ln (x)

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

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

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