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Derivative of:
Derivative of 3*x^5-2*x^2
Derivative of 2^x*sin(x)
Derivative of (1/x)^x
Derivative of x-ln(1+x)
Identical expressions
zero . two x^ five - zero .25x^2+sqrt5
0.2x to the power of 5 minus 0.25x squared plus square root of 5
zero . two x to the power of five minus zero .25x squared plus square root of 5
0.2x^5-0.25x^2+√5
0.2x5-0.25x2+sqrt5
0.2x⁵-0.25x²+sqrt5
0.2x to the power of 5-0.25x to the power of 2+sqrt5
Similar expressions
0.2x^5+0.25x^2+sqrt5
0.2x^5-0.25x^2-sqrt5

The derivative of the function/ 0.2x^5-0.25x^2+sqrt5

Derivative of 0.2x^5-0.25x^2+sqrt5

The solution

You have entered [src]

 5    2        
x    x      ___
-- - -- + \/ 5 
5    4

$$\left(\frac{x^{5}}{5} - \frac{x^{2}}{4}\right) + \sqrt{5}$$

x^5/5 - x^2/4 + sqrt(5)

Detail solution

Differentiate $\left(\frac{x^{5}}{5} - \frac{x^{2}}{4}\right) + \sqrt{5}$ term by term:
1. Differentiate $\frac{x^{5}}{5} - \frac{x^{2}}{4}$ 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: $x^{5}$ goes to $5 x^{4}$
    So, the result is: $x^{4}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $- \frac{x}{2}$
  The result is: $x^{4} - \frac{x}{2}$
2. The derivative of the constant $\sqrt{5}$ is zero.
The result is: $x^{4} - \frac{x}{2}$

The answer is:

$x^{4} - \frac{x}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 4   x
x  - -
     2

$$x^{4} - \frac{x}{2}$$

Simplify

The second derivative [src]

  1      3
- - + 4*x 
  2

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

Simplify

The third derivative [src]

    2
12*x

$$12 x^{2}$$

Simplify