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Derivative of:
Derivative of x^4-8x^2
Derivative of dy/dx
Derivative of log0,5(x)
Derivative of y=sqrt(cos3x)
Graphing y =:
x^4-8x^2
Identical expressions
x^ four -8x^ two
x to the power of 4 minus 8x squared
x to the power of four minus 8x to the power of two
x4-8x2
x⁴-8x²
x to the power of 4-8x to the power of 2
Similar expressions
f(x)=x^4-8x^2+5
x^4+8x^2

The derivative of the function/ x^4-8x^2

Derivative of x^4-8x^2

The solution

You have entered [src]

 4      2
x  - 8*x

$$x^{4} - 8 x^{2}$$

d / 4      2\
--\x  - 8*x /
dx

$$\frac{d}{d x} \left(x^{4} - 8 x^{2}\right)$$

Transform

Detail solution

Differentiate $x^{4} - 8 x^{2}$ 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. 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: $16 x$
  So, the result is: $- 16 x$
The result is: $4 x^{3} - 16 x$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           3
-16*x + 4*x

$$4 x^{3} - 16 x$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify

The graph

Derivative of x^4-8x^2