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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 4 z + z 1 - z^{2} d z

- 5 e^{x}

\int \frac{x ^{6}}{( 6 - x ^{7} ) ^{2}} d x

x \to 7 lim (∣ x - 7 ∣)

h (x) = x

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