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Derivative of:
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Identical expressions
sqrt(x)^ three + one
square root of (x) cubed plus 1
square root of (x) to the power of three plus one
√(x)^3+1
sqrt(x)3+1
sqrtx3+1
sqrt(x)³+1
sqrt(x) to the power of 3+1
sqrtx^3+1
Similar expressions
sqrt(x)^3-1

The derivative of the function/ sqrt(x)^3+1

Derivative of sqrt(x)^3+1

The solution

You have entered [src]

     3    
  ___     
\/ x   + 1

$$\left(\sqrt{x}\right)^{3} + 1$$

(sqrt(x))^3 + 1

Detail solution

Differentiate $\left(\sqrt{x}\right)^{3} + 1$ term by term:
1. Let $u = \sqrt{x}$ .
2. Apply the power rule: $u^{3}$ goes to $3 u^{2}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{x}$ :
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  The result of the chain rule is:
  
  $\frac{3 \sqrt{x}}{2}$
4. The derivative of the constant $1$ is zero.
The result is: $\frac{3 \sqrt{x}}{2}$

The answer is:

$\frac{3 \sqrt{x}}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   3/2
3*x   
------
 2*x

$$\frac{3 x^{\frac{3}{2}}}{2 x}$$

Simplify

The second derivative [src]

   3   
-------
    ___
4*\/ x

$$\frac{3}{4 \sqrt{x}}$$

Simplify

The third derivative [src]

 -3   
------
   3/2
8*x

$$- \frac{3}{8 x^{\frac{3}{2}}}$$

Simplify

The graph

Derivative of sqrt(x)^3+1