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Derivative of 2x^8+8x^3-5

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

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   8      3    
2*x  + 8*x  - 5
(2x8+8x3)5\left(2 x^{8} + 8 x^{3}\right) - 5
2*x^8 + 8*x^3 - 5
Detail solution
  1. Differentiate (2x8+8x3)5\left(2 x^{8} + 8 x^{3}\right) - 5 term by term:

    1. Differentiate 2x8+8x32 x^{8} + 8 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: x8x^{8} goes to 8x78 x^{7}

        So, the result is: 16x716 x^{7}

      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: 24x224 x^{2}

      The result is: 16x7+24x216 x^{7} + 24 x^{2}

    2. The derivative of the constant 5-5 is zero.

    The result is: 16x7+24x216 x^{7} + 24 x^{2}

  2. Now simplify:

    x2(16x5+24)x^{2} \left(16 x^{5} + 24\right)


The answer is:

x2(16x5+24)x^{2} \left(16 x^{5} + 24\right)

The graph
02468-8-6-4-2-1010-500000000500000000
The first derivative [src]
    7       2
16*x  + 24*x 
16x7+24x216 x^{7} + 24 x^{2}
The second derivative [src]
     /       5\
16*x*\3 + 7*x /
16x(7x5+3)16 x \left(7 x^{5} + 3\right)
The third derivative [src]
   /        5\
48*\1 + 14*x /
48(14x5+1)48 \left(14 x^{5} + 1\right)