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

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

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

The graph:

from to

Piecewise:

The solution

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

  1. Differentiate 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: goes to

      So, the result is:

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

      1. Apply the power rule: goes to

      So, the result is:

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

      1. Apply the power rule: goes to

      So, the result is:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
              3
5 + 4*x + 20*x
$$20 x^{3} + 4 x + 5$$
Simplify
The second derivative [src] 
  /        2\
4*\1 + 15*x /
$$4 \cdot \left(15 x^{2} + 1\right)$$
Simplify
The third derivative [src] 
120*x
$$120 x$$
Simplify
3-th derivative [src] 
120*x
$$120 x$$
Simplify
The graph
Derivative of 5x^4+2x^2+5x
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