Mister Exam

Lang:

The derivative of the function/ x+x^3-5x

Derivative of x+x^3-5x

The solution

You have entered [src]

     3      
x + x  - 5*x

$$x^{3} - 5 x + x$$

d /     3      \
--\x + x  - 5*x/
dx

$$\frac{d}{d x} \left(x^{3} - 5 x + x\right)$$

Transform

Detail solution

Differentiate $x^{3} - 5 x + x$ term by term:
1. Apply the power rule: $x$ goes to $1$
2. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
3. 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: $x$ goes to $1$
    So, the result is: $5$
  So, the result is: $-5$
The result is: $3 x^{2} - 4$

The answer is:

$3 x^{2} - 4$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        2
-4 + 3*x

$$3 x^{2} - 4$$

Simplify

The second derivative [src]

6*x

$$6 x$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of x+x^3-5x