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The derivative of the function/ sgrtx-9x^2

Derivative of sgrtx-9x^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  ___      2
\/ x  - 9*x
$$\sqrt{x} - 9 x^{2}$$ 
sqrt(x) - 9*x^2
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          
------- - 18*x
    ___       
2*\/ x
$$- 18 x + \frac{1}{2 \sqrt{x}}$$
Simplify
The second derivative [src] 
 /       1   \
-|18 + ------|
 |        3/2|
 \     4*x   /
$$- (18 + \frac{1}{4 x^{\frac{3}{2}}})$$
Simplify
The third derivative [src] 
  3   
------
   5/2
8*x
$$\frac{3}{8 x^{\frac{5}{2}}}$$
Simplify
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