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Derivative of:
Derivative of (sin(x))^2
Derivative of x-1
Derivative of sin(x)/cos(x)
Derivative of sin(x)/x^2
Factor polynomial:
x^3-x^5
Identical expressions
x^ three -x^ five
x cubed minus x to the power of 5
x to the power of three minus x to the power of five
x3-x5
x³-x⁵
x to the power of 3-x to the power of 5
Similar expressions
x^3+x^5

The derivative of the function/ x^3-x^5

Derivative of x^3-x^5

The solution

You have entered [src]

 3    5
x  - x

$$- x^{5} + x^{3}$$

x^3 - x^5

Detail solution

Differentiate $- x^{5} + x^{3}$ term by term:
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
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: $- 5 x^{4}$
The result is: $- 5 x^{4} + 3 x^{2}$
Now simplify:

$x^{2} \left(3 - 5 x^{2}\right)$

The answer is:

$x^{2} \left(3 - 5 x^{2}\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     4      2
- 5*x  + 3*x

$$- 5 x^{4} + 3 x^{2}$$

Simplify

The second derivative [src]

    /        2\
2*x*\3 - 10*x /

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

Simplify

The third derivative [src]

  /        2\
6*\1 - 10*x /

$$6 \left(1 - 10 x^{2}\right)$$

Simplify

The graph

Derivative of x^3-x^5