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y=√x+3x^6
The derivative of the function/ y=√x+3x^6

Derivative of y=√x+3x^6

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  ___      6
\/ x  + 3*x
$$\sqrt{x} + 3 x^{6}$$
Transform
Detail solution

  1. Differentiate term by term:

    1. Apply the power rule: goes to

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   1          5
------- + 18*x 
    ___        
2*\/ x
$$18 x^{5} + \frac{1}{2 \sqrt{x}}$$
Simplify
The second derivative [src] 
    4     1   
90*x  - ------
           3/2
        4*x
$$90 x^{4} - \frac{1}{4 x^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
  /     3     1   \
3*|120*x  + ------|
  |            5/2|
  \         8*x   /
$$3 \left(120 x^{3} + \frac{1}{8 x^{\frac{5}{2}}}\right)$$
Simplify
The graph
Derivative of y=√x+3x^6
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