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(x^2-1)(x^4+2)
The derivative of the function/ (x^2-1)(x^4+2)

Derivative of (x^2-1)(x^4+2)

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

from to

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The solution

You have entered [src] 
/ 2    \ / 4    \
\x  - 1/*\x  + 2/
(x2−1)(x4+2)\left(x^{2} - 1\right) \left(x^{4} + 2\right) 
(x^2 - 1)*(x^4 + 2)
Detail solution

  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

    f(x)=x2−1f{\left(x \right)} = x^{2} - 1; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Differentiate x2−1x^{2} - 1 term by term:

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      2. The derivative of the constant −1-1 is zero.

      The result is: 2x2 x

    g(x)=x4+2g{\left(x \right)} = x^{4} + 2; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Differentiate x4+2x^{4} + 2 term by term:

      1. Apply the power rule: x4x^{4} goes to 4x34 x^{3}

      2. The derivative of the constant 22 is zero.

      The result is: 4x34 x^{3}

    The result is: 4x3(x2−1)+2x(x4+2)4 x^{3} \left(x^{2} - 1\right) + 2 x \left(x^{4} + 2\right)

  2. Now simplify:

    6x5−4x3+4x6 x^{5} - 4 x^{3} + 4 x

The answer is:

6x5−4x3+4x6 x^{5} - 4 x^{3} + 4 x

The graph
02468-8-6-4-2-1010-20000002000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    / 4    \      3 / 2    \
2*x*\x  + 2/ + 4*x *\x  - 1/
4x3(x2−1)+2x(x4+2)4 x^{3} \left(x^{2} - 1\right) + 2 x \left(x^{4} + 2\right)
Simplify
The second derivative [src] 
  /       4      2 /      2\\
2*\2 + 9*x  + 6*x *\-1 + x //
2(9x4+6x2(x2−1)+2)2 \left(9 x^{4} + 6 x^{2} \left(x^{2} - 1\right) + 2\right)
Simplify
The third derivative [src] 
     /        2\
24*x*\-1 + 5*x /
24x(5x2−1)24 x \left(5 x^{2} - 1\right)
Simplify
The graph
Derivative of (x^2-1)(x^4+2)
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