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Derivative of:
Derivative of e^-1
Derivative of e^x*cosx
Derivative of 6*x^3
Derivative of 5*tan(x)
Identical expressions
y=sqrtx+4x^ three - six
y equally square root of x plus 4x cubed minus 6
y equally square root of x plus 4x to the power of three minus six
y=√x+4x^3-6
y=sqrtx+4x3-6
y=sqrtx+4x³-6
y=sqrtx+4x to the power of 3-6
Similar expressions
y=sqrtx+4x^3+6
y=sqrtx-4x^3-6

The derivative of the function/ y=sqrtx+4x^3-6

Derivative of y=sqrtx+4x^3-6

The solution

You have entered [src]

  ___      3    
\/ x  + 4*x  - 6

$$\left(\sqrt{x} + 4 x^{3}\right) - 6$$

sqrt(x) + 4*x^3 - 6

Detail solution

Differentiate $\left(\sqrt{x} + 4 x^{3}\right) - 6$ term by term:
1. Differentiate $\sqrt{x} + 4 x^{3}$ 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: $12 x^{2}$
  The result is: $12 x^{2} + \frac{1}{2 \sqrt{x}}$
2. The derivative of the constant $-6$ is zero.
The result is: $12 x^{2} + \frac{1}{2 \sqrt{x}}$

The answer is:

$12 x^{2} + \frac{1}{2 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   1          2
------- + 12*x 
    ___        
2*\/ x

$$12 x^{2} + \frac{1}{2 \sqrt{x}}$$

Simplify

The second derivative [src]

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

$$24 x - \frac{1}{4 x^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of y=sqrtx+4x^3-6