What is the derivative of 4/(x+2sqrt(x)) ?

The derivative of 4/(x+2sqrt(x)) is -(4(sqrt(x)+1))/(sqrt(x)(x+2\sqrt{x))^2}

What is the first derivative of 4/(x+2sqrt(x)) ?

The first derivative of 4/(x+2sqrt(x)) is -(4(sqrt(x)+1))/(sqrt(x)(x+2\sqrt{x))^2}

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\frac{d}{d x} (\frac{4}{x + 2 x})

- \frac{4 ( x + 1 )}{x ( x + 2 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4}{x + 2 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (\frac{1}{x + 2 x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 4 \frac{d}{d x} ((x + 2 x)^{- 1})

Apply the chain rule:

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

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

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

= 4 (- \frac{1}{( x + 2 x ) ^{2}} (1 + \frac{1}{x}))

Simplify

4 (- \frac{1}{( x + 2 x ) ^{2}} (1 + \frac{1}{x})) : - \frac{4 ( x + 1 )}{x ( x + 2 x ) ^{2}}

= - \frac{4 ( x + 1 )}{x ( x + 2 x ) ^{2}}

What is the derivative of 4/(x+2sqrt(x)) ?
The derivative of 4/(x+2sqrt(x)) is -(4(sqrt(x)+1))/(sqrt(x)(x+2\sqrt{x))^2}
What is the first derivative of 4/(x+2sqrt(x)) ?
The first derivative of 4/(x+2sqrt(x)) is -(4(sqrt(x)+1))/(sqrt(x)(x+2\sqrt{x))^2}