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x^4-6x^2+5
The derivative of the function/ x^4-6x^2+5

Derivative of x^4-6x^2+5

Function f() - derivative -N order at the point
v

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Piecewise:

The solution

You have entered [src] 
 4      2    
x  - 6*x  + 5
x4−6x2+5x^{4} - 6 x^{2} + 5 
d / 4      2    \
--\x  - 6*x  + 5/
dx
ddx(x4−6x2+5)\frac{d}{d x} \left(x^{4} - 6 x^{2} + 5\right)
Transform
Detail solution

  1. Differentiate x4−6x2+5x^{4} - 6 x^{2} + 5 term by term:

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

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of a constant times a function is the constant times the derivative of the function.

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

        So, the result is: 12x12 x

      So, the result is: −12x- 12 x

    3. The derivative of the constant 55 is zero.

    The result is: 4x3−12x4 x^{3} - 12 x

  2. Now simplify:

    4x(x2−3)4 x \left(x^{2} - 3\right)

The answer is:

4x(x2−3)4 x \left(x^{2} - 3\right)

The graph
02468-8-6-4-2-1010-1000010000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
           3
-12*x + 4*x
4x3−12x4 x^{3} - 12 x
Simplify
The second derivative [src] 
   /      2\
12*\-1 + x /
12(x2−1)12 \left(x^{2} - 1\right)
Simplify
The third derivative [src] 
24*x
24x24 x
Simplify
The graph
Derivative of x^4-6x^2+5
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