What is the derivative of (1+sqrt(x))^3 ?

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

What is the first derivative of (1+sqrt(x))^3 ?

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

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derivative of

(1 + x)^{3}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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