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

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

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

The solution

You have entered [src]

 4      2    
x  - 5*x  + 4

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

x^4 - 5*x^2 + 4

Detail solution

Differentiate $\left(x^{4} - 5 x^{2}\right) + 4$ term by term:
1. Differentiate $x^{4} - 5 x^{2}$ 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: $- 10 x$
  The result is: $4 x^{3} - 10 x$
2. The derivative of the constant $4$ is zero.
The result is: $4 x^{3} - 10 x$

The answer is:

$4 x^{3} - 10 x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           3
-10*x + 4*x

$$4 x^{3} - 10 x$$

Simplify

The second derivative [src]

  /        2\
2*\-5 + 6*x /

$$2 \left(6 x^{2} - 5\right)$$

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify

The graph

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