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Derivative of:
Derivative of -1
Derivative of 1/e^x
Derivative of x^4-x^9
Derivative of sqrt(x)*sin(x)
Graphing y =:
x^4-x^9
Identical expressions
x^ four -x^ nine
x to the power of 4 minus x to the power of 9
x to the power of four minus x to the power of nine
x4-x9
x⁴-x⁹
Similar expressions
x^4+x^9

The derivative of the function/ x^4-x^9

Derivative of x^4-x^9

The solution

You have entered [src]

 4    9
x  - x

$$- x^{9} + x^{4}$$

d / 4    9\
--\x  - x /
dx

$$\frac{d}{d x} \left(- x^{9} + x^{4}\right)$$

Transform

Detail solution

Differentiate $- x^{9} + x^{4}$ 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: $x^{9}$ goes to $9 x^{8}$
  So, the result is: $- 9 x^{8}$
The result is: $- 9 x^{8} + 4 x^{3}$
Now simplify:

$x^{3} \cdot \left(4 - 9 x^{5}\right)$

The answer is:

$x^{3} \cdot \left(4 - 9 x^{5}\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     8      3
- 9*x  + 4*x

$$- 9 x^{8} + 4 x^{3}$$

Simplify

The second derivative [src]

    2 /       5\
12*x *\1 - 6*x /

$$12 x^{2} \cdot \left(1 - 6 x^{5}\right)$$

Simplify

The third derivative [src]

     /        5\
24*x*\1 - 21*x /

$$24 x \left(1 - 21 x^{5}\right)$$

Simplify

The graph

Derivative of x^4-x^9