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Derivative of:
Derivative of u
Derivative of e^x/x^2
Derivative of cos(x)/x^2
Derivative of cos(sqrt(x))
Graphing y =:
x^4-8x^2+7
Identical expressions
x^ four -8x^ two + seven
x to the power of 4 minus 8x squared plus 7
x to the power of four minus 8x to the power of two plus seven
x4-8x2+7
x⁴-8x²+7
x to the power of 4-8x to the power of 2+7
Similar expressions
x^4+8x^2+7
x^4-8x^2-7

The derivative of the function/ x^4-8x^2+7

Derivative of x^4-8x^2+7

The solution

You have entered [src]

 4      2    
x  - 8*x  + 7

$$\left(x^{4} - 8 x^{2}\right) + 7$$

x^4 - 8*x^2 + 7

Detail solution

Differentiate $\left(x^{4} - 8 x^{2}\right) + 7$ term by term:
1. 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. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $- 16 x$
  The result is: $4 x^{3} - 16 x$
2. The derivative of the constant $7$ is zero.
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 /

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

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify