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5x^4-3x^2+5
The derivative of the function/ 5x^4-3x^2+5

Derivative of 5x^4-3x^2+5

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

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The solution

You have entered [src] 
   4      2    
5*x  - 3*x  + 5
5x4−3x2+55 x^{4} - 3 x^{2} + 5 
d /   4      2    \
--\5*x  - 3*x  + 5/
dx
ddx(5x4−3x2+5)\frac{d}{d x} \left(5 x^{4} - 3 x^{2} + 5\right)
Transform
Detail solution

  1. Differentiate 5x4−3x2+55 x^{4} - 3 x^{2} + 5 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: x4x^{4} goes to 4x34 x^{3}

      So, the result is: 20x320 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: 6x6 x

      So, the result is: −6x- 6 x

    3. The derivative of the constant 55 is zero.

    The result is: 20x3−6x20 x^{3} - 6 x

The answer is:

20x3−6x20 x^{3} - 6 x

The graph
02468-8-6-4-2-1010-100000100000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
           3
-6*x + 20*x
20x3−6x20 x^{3} - 6 x
Simplify
The second derivative [src] 
  /         2\
6*\-1 + 10*x /
6⋅(10x2−1)6 \cdot \left(10 x^{2} - 1\right)
Simplify
The third derivative [src] 
120*x
120x120 x
Simplify
The graph
Derivative of 5x^4-3x^2+5
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