What is the derivative of y= x/((x+1)^{1/2)} ?

The derivative of y= x/((x+1)^{1/2)} is (x+2)/(2(x+1)^{3/2)}

What is the first derivative of y= x/((x+1)^{1/2)} ?

The first derivative of y= x/((x+1)^{1/2)} is (x+2)/(2(x+1)^{3/2)}

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

2^{u}

\frac{1}{lo g _{3} ( 1 - 2 x )}

\frac{d}{d t} (t^{2} + t^{3})

\frac{d}{d t} (3 t^{2} - 5 cos^{3} (t))

\frac{d}{d x} (2 cos (3 x) + 2 sin (10 y) + 3 x - 10 y)

What is the derivative of y= x/((x+1)^{1/2)} ?
The derivative of y= x/((x+1)^{1/2)} is (x+2)/(2(x+1)^{3/2)}
What is the first derivative of y= x/((x+1)^{1/2)} ?
The first derivative of y= x/((x+1)^{1/2)} is (x+2)/(2(x+1)^{3/2)}