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Derivative of:
Derivative of (x^2+1)/x
Derivative of x^2*atanh(x)*acoth(x)
Derivative of 4x^2
Derivative of sqrt(x^3)
Graphing y =:
x^4-6x^2+5
Identical expressions
x^ four -6x^ two + five
x to the power of 4 minus 6x squared plus 5
x to the power of four minus 6x to the power of two plus five
x4-6x2+5
x⁴-6x²+5
x to the power of 4-6x to the power of 2+5
Similar expressions
x^4-6x^2-5
x^4+6x^2+5

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

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

The solution

You have entered [src]

 4      2    
x  - 6*x  + 5

$$x^{4} - 6 x^{2} + 5$$

d / 4      2    \
--\x  - 6*x  + 5/
dx

$$\frac{d}{d x} \left(x^{4} - 6 x^{2} + 5\right)$$

Transform

Detail solution

Differentiate $x^{4} - 6 x^{2} + 5$ 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. 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: $12 x$
  So, the result is: $- 12 x$
3. The derivative of the constant $5$ is zero.
The result is: $4 x^{3} - 12 x$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           3
-12*x + 4*x

$$4 x^{3} - 12 x$$

Simplify

The second derivative [src]

   /      2\
12*\-1 + x /

$$12 \left(x^{2} - 1\right)$$

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify

The graph

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