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-30*x^6+18*x-3*sqrt(x)+1
The derivative of the function/ -30*x^6+18*x-3*sqrt(x)+1

Derivative of -30*x^6+18*x-3*sqrt(x)+1

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
      6              ___    
- 30*x  + 18*x - 3*\/ x  + 1
$$- 3 \sqrt{x} - 30 x^{6} + 18 x + 1$$ 
d /      6              ___    \
--\- 30*x  + 18*x - 3*\/ x  + 1/
dx
$$\frac{d}{d x} \left(- 3 \sqrt{x} - 30 x^{6} + 18 x + 1\right)$$
Transform
Detail solution

  1. Differentiate term by term:

    1. 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:

    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:

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

      1. 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:

      So, the result is:

    4. The derivative of the constant is zero.

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
          5      3   
18 - 180*x  - -------
                  ___
              2*\/ x
$$- 180 x^{5} + 18 - \frac{3}{2 \sqrt{x}}$$
Simplify
The second derivative [src] 
  /       4     1   \
3*|- 300*x  + ------|
  |              3/2|
  \           4*x   /
$$3 \left(- 300 x^{4} + \frac{1}{4 x^{\frac{3}{2}}}\right)$$
Simplify
The third derivative [src] 
   /     3     1   \
-9*|400*x  + ------|
   |            5/2|
   \         8*x   /
$$- 9 \cdot \left(400 x^{3} + \frac{1}{8 x^{\frac{5}{2}}}\right)$$
Simplify
The graph
Derivative of -30*x^6+18*x-3*sqrt(x)+1
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