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Derivative of:
Derivative of 3x^2-5x+5
Derivative of (2*x-1)^2
Derivative of 2*x^3-3*x^2+6*x+1
Derivative of (2x+3)^2
Identical expressions
sqrt(x)+ three *x^ three
square root of (x) plus 3 multiply by x cubed
square root of (x) plus three multiply by x to the power of three
√(x)+3*x^3
sqrt(x)+3*x3
sqrtx+3*x3
sqrt(x)+3*x³
sqrt(x)+3*x to the power of 3
sqrt(x)+3x^3
sqrt(x)+3x3
sqrtx+3x3
sqrtx+3x^3
Similar expressions
sqrt(x)-3*x^3

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

Derivative of sqrt(x)+3*x^3

The solution

You have entered [src]

  ___      3
\/ x  + 3*x

$$\sqrt{x} + 3 x^{3}$$

sqrt(x) + 3*x^3

Detail solution

Differentiate $\sqrt{x} + 3 x^{3}$ term by term:
1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $9 x^{2}$
The result is: $9 x^{2} + \frac{1}{2 \sqrt{x}}$

The answer is:

$9 x^{2} + \frac{1}{2 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   1         2
------- + 9*x 
    ___       
2*\/ x

$$9 x^{2} + \frac{1}{2 \sqrt{x}}$$

Simplify

The second derivative [src]

         1   
18*x - ------
          3/2
       4*x

$$18 x - \frac{1}{4 x^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

  /      1   \
3*|6 + ------|
  |       5/2|
  \    8*x   /

$$3 \left(6 + \frac{1}{8 x^{\frac{5}{2}}}\right)$$

Simplify

The graph

Derivative of sqrt(x)+3*x^3