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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

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The solution

You have entered [src] 
  ___      6
\/ x  + 3*x
x+3x6\sqrt{x} + 3 x^{6}
Transform
Detail solution

  1. Differentiate x+3x6\sqrt{x} + 3 x^{6} term by term:

    1. Apply the power rule: x\sqrt{x} goes to 12x\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: x6x^{6} goes to 6x56 x^{5}

      So, the result is: 18x518 x^{5}

    The result is: 18x5+12x18 x^{5} + \frac{1}{2 \sqrt{x}}

The answer is:

18x5+12x18 x^{5} + \frac{1}{2 \sqrt{x}}

The graph
02468-8-6-4-2-1010-50000005000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   1          5
------- + 18*x 
    ___        
2*\/ x
18x5+12x18 x^{5} + \frac{1}{2 \sqrt{x}}
Simplify
The second derivative [src] 
    4     1   
90*x  - ------
           3/2
        4*x
90x4−14x3290 x^{4} - \frac{1}{4 x^{\frac{3}{2}}}
Simplify
The third derivative [src] 
  /     3     1   \
3*|120*x  + ------|
  |            5/2|
  \         8*x   /
3(120x3+18x52)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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