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(x^2-x)*(x^3+x)

How to use it?
Derivative of:
Derivative of 6
Derivative of x^7*e^x
Derivative of 6^x
Derivative of 1/(x+1)^2
Identical expressions
(x^ two -x)*(x^ three +x)
(x squared minus x) multiply by (x cubed plus x)
(x to the power of two minus x) multiply by (x to the power of three plus x)
(x2-x)*(x3+x)
x2-x*x3+x
(x²-x)*(x³+x)
(x to the power of 2-x)*(x to the power of 3+x)
(x^2-x)(x^3+x)
(x2-x)(x3+x)
x2-xx3+x
x^2-xx^3+x
Similar expressions
(x^2+x)*(x^3+x)
(x^2-x)*(x^3-x)

The derivative of the function/ (x^2-x)*(x^3+x)

Derivative of (x^2-x)*(x^3+x)

The solution

You have entered [src]

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

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

d // 2    \ / 3    \\
--\\x  - x/*\x  + x//
dx

$$\frac{d}{d x} \left(x^{2} - x\right) \left(x^{3} + x\right)$$

Transform

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x^{2} - x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{2} - x$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. 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: $-1$
  The result is: $2 x - 1$
$g{\left(x \right)} = x^{3} + x$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x^{3} + x$ term by term:
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  2. Apply the power rule: $x$ goes to $1$
  The result is: $3 x^{2} + 1$
The result is: $\left(2 x - 1\right) \left(x^{3} + x\right) + \left(x^{2} - x\right) \left(3 x^{2} + 1\right)$
Now simplify:

$x \left(5 x^{3} - 4 x^{2} + 3 x - 2\right)$

The answer is:

$x \left(5 x^{3} - 4 x^{2} + 3 x - 2\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

/       2\ / 2    \              / 3    \
\1 + 3*x /*\x  - x/ + (-1 + 2*x)*\x  + x/

$$\left(2 x - 1\right) \left(x^{3} + x\right) + \left(x^{2} - x\right) \left(3 x^{2} + 1\right)$$

Simplify

The second derivative [src]

  /     3   /       2\                 2         \
2*\x + x  + \1 + 3*x /*(-1 + 2*x) + 3*x *(-1 + x)/

$$2 \left(x^{3} + 3 x^{2} \left(x - 1\right) + x + \left(2 x - 1\right) \left(3 x^{2} + 1\right)\right)$$

Simplify

The third derivative [src]

  /           2                 \
6*\1 - x + 4*x  + 3*x*(-1 + 2*x)/

$$6 \cdot \left(4 x^{2} + 3 x \left(2 x - 1\right) - x + 1\right)$$

Simplify

The graph

Derivative of (x^2-x)*(x^3+x)