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

Derivative of 3x^5-5x^3

Function f() - derivative -N order at the point
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The graph:

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The solution

You have entered [src] 
   5      3
3*x  - 5*x
3x5−5x33 x^{5} - 5 x^{3} 
3*x^5 - 5*x^3
Detail solution

  1. Differentiate 3x5−5x33 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: x5x^{5} goes to 5x45 x^{4}

      So, the result is: 15x415 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: x3x^{3} goes to 3x23 x^{2}

      So, the result is: −15x2- 15 x^{2}

    The result is: 15x4−15x215 x^{4} - 15 x^{2}

  2. Now simplify:

    15x2(x2−1)15 x^{2} \left(x^{2} - 1\right)

The answer is:

15x2(x2−1)15 x^{2} \left(x^{2} - 1\right)

The graph
02468-8-6-4-2-1010-500000500000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      2       4
- 15*x  + 15*x
15x4−15x215 x^{4} - 15 x^{2}
Simplify
The second derivative [src] 
     /        2\
30*x*\-1 + 2*x /
30x(2x2−1)30 x \left(2 x^{2} - 1\right)
Simplify
The third derivative [src] 
   /        2\
30*\-1 + 6*x /
30(6x2−1)30 \left(6 x^{2} - 1\right)
Simplify
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