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Derivative of:
Derivative of -2x/(1+x^2)^2
Derivative of 3*sin(x)^(2)
Derivative of log(secx+tanx)
Derivative of ln(3x-2)
Graphing y =:
x^4-2x^5+5
Identical expressions
x^ four -2x^ five + five
x to the power of 4 minus 2x to the power of 5 plus 5
x to the power of four minus 2x to the power of five plus five
x4-2x5+5
x⁴-2x⁵+5
Similar expressions
x^4+2x^5+5
x^4-2x^5-5

The derivative of the function/ x^4-2x^5+5

Derivative of x^4-2x^5+5

The solution

You have entered [src]

 4      5    
x  - 2*x  + 5

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

x^4 - 2*x^5 + 5

Detail solution

Differentiate $\left(- 2 x^{5} + x^{4}\right) + 5$ term by term:
1. Differentiate $- 2 x^{5} + x^{4}$ term by term:
  1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
  2. 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: $- 10 x^{4}$
  The result is: $- 10 x^{4} + 4 x^{3}$
2. The derivative of the constant $5$ is zero.
The result is: $- 10 x^{4} + 4 x^{3}$
Now simplify:

$x^{3} \left(4 - 10 x\right)$

The answer is:

$x^{3} \left(4 - 10 x\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      4      3
- 10*x  + 4*x

$$- 10 x^{4} + 4 x^{3}$$

Simplify

The second derivative [src]

   2           
4*x *(3 - 10*x)

$$4 x^{2} \left(3 - 10 x\right)$$

Simplify

The third derivative [src]

24*x*(1 - 5*x)

$$24 x \left(1 - 5 x\right)$$

Simplify