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Derivative of:
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Graphing y =:
x^4+2x^2+5
Identical expressions
y=x^ four + two x^2+ five
y equally x to the power of 4 plus 2x squared plus 5
y equally x to the power of four plus two x squared plus five
y=x4+2x2+5
y=x⁴+2x²+5
y=x to the power of 4+2x to the power of 2+5
Similar expressions
y=x^4-2x^2+5
y=x^4+2x^2-5

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

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

The solution

You have entered [src]

 4      2    
x  + 2*x  + 5

$$\left(x^{4} + 2 x^{2}\right) + 5$$

x^4 + 2*x^2 + 5

Detail solution

Differentiate $\left(x^{4} + 2 x^{2}\right) + 5$ term by term:
1. Differentiate $x^{4} + 2 x^{2}$ term by term:
  1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $4 x$
  The result is: $4 x^{3} + 4 x$
2. The derivative of the constant $5$ is zero.
The result is: $4 x^{3} + 4 x$
Now simplify:

$4 x \left(x^{2} + 1\right)$

The answer is:

$4 x \left(x^{2} + 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

         3
4*x + 4*x

$$4 x^{3} + 4 x$$

Simplify

The second derivative [src]

  /       2\
4*\1 + 3*x /

$$4 \left(3 x^{2} + 1\right)$$

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify

The graph

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