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Derivative of:
Derivative of 2x²
Derivative of f(x)=1
Derivative of e^x*x^2
Derivative of 2*sqrt(x^3)
Identical expressions
x^ five - six *x^ three
x to the power of 5 minus 6 multiply by x cubed
x to the power of five minus six multiply by x to the power of three
x5-6*x3
x⁵-6*x³
x to the power of 5-6*x to the power of 3
x^5-6x^3
x5-6x3
Similar expressions
x^5+6*x^3

The derivative of the function/ x^5-6*x^3

Derivative of x^5-6*x^3

The solution

You have entered [src]

 5      3
x  - 6*x

$$x^{5} - 6 x^{3}$$

x^5 - 6*x^3

Detail solution

Differentiate $x^{5} - 6 x^{3}$ term by term:
1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $- 18 x^{2}$
The result is: $5 x^{4} - 18 x^{2}$
Now simplify:

$x^{2} \left(5 x^{2} - 18\right)$

The answer is:

$x^{2} \left(5 x^{2} - 18\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      2      4
- 18*x  + 5*x

$$5 x^{4} - 18 x^{2}$$

Simplify

The second derivative [src]

    /        2\
4*x*\-9 + 5*x /

$$4 x \left(5 x^{2} - 9\right)$$

Simplify

The third derivative [src]

   /        2\
12*\-3 + 5*x /

$$12 \left(5 x^{2} - 3\right)$$

Simplify

The graph

Derivative of x^5-6*x^3