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Derivative of:
Derivative of x^(4/3)
Derivative of x*2^x
Derivative of (x^2)/36
Derivative of x+log(x)
Graphing y =:
-x^4+4x^2-5
Identical expressions
-x^ four +4x^ two - five
minus x to the power of 4 plus 4x squared minus 5
minus x to the power of four plus 4x to the power of two minus five
-x4+4x2-5
-x⁴+4x²-5
-x to the power of 4+4x to the power of 2-5
Similar expressions
-x^4-4x^2-5
x^4+4x^2-5
-x^4+4x^2+5

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

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

The solution

You have entered [src]

   4      2    
- x  + 4*x  - 5

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

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

Detail solution

Differentiate $\left(- x^{4} + 4 x^{2}\right) - 5$ term by term:
1. Differentiate $- x^{4} + 4 x^{2}$ 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: $x^{4}$ goes to $4 x^{3}$
    So, the result is: $- 4 x^{3}$
  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: $8 x$
  The result is: $- 4 x^{3} + 8 x$
2. The derivative of the constant $-5$ is zero.
The result is: $- 4 x^{3} + 8 x$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     3      
- 4*x  + 8*x

$$- 4 x^{3} + 8 x$$

Simplify

The second derivative [src]

  /       2\
4*\2 - 3*x /

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

Simplify

The third derivative [src]

-24*x

$$- 24 x$$

Simplify