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Derivative of:
Derivative of x^(1/3)
Derivative of 1/sqrt(x)
Derivative of x*acot(x)
Derivative of 4/x
Graphing y =:
3x^5-5x^3
Identical expressions
three x^ five -5x^3
3x to the power of 5 minus 5x cubed
three x to the power of five minus 5x cubed
3x5-5x3
3x⁵-5x³
3x to the power of 5-5x to the power of 3
Similar expressions
3x^5+5x^3

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

Derivative of 3x^5-5x^3

The solution

You have entered [src]

   5      3
3*x  - 5*x

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

3*x^5 - 5*x^3

Detail solution

Differentiate $3 x^{5} - 5 x^{3}$ 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: $15 x^{4}$
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: $- 15 x^{2}$
The result is: $15 x^{4} - 15 x^{2}$
Now simplify:

$15 x^{2} \left(x^{2} - 1\right)$

The answer is:

$15 x^{2} \left(x^{2} - 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      2       4
- 15*x  + 15*x

$$15 x^{4} - 15 x^{2}$$

Simplify

The second derivative [src]

     /        2\
30*x*\-1 + 2*x /

$$30 x \left(2 x^{2} - 1\right)$$

Simplify

The third derivative [src]

   /        2\
30*\-1 + 6*x /

$$30 \left(6 x^{2} - 1\right)$$

Simplify