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Expressões idênticas
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y=x^22x-1
Expressões semelhantes
y=x^2(2x+1)

Derivada de função/ y=x^2(2x-1)

Derivada y=x^2(2x-1)

A solução

You have entered [src]

 2          
x *(2*x - 1)

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

x^2*(2*x - 1)

Detail solution

Apply the product rule:

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

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

$2 x \left(3 x - 1\right)$

The answer is:

$2 x \left(3 x - 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2                
2*x  + 2*x*(2*x - 1)

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

Simplify

The second derivative [src]

2*(-1 + 6*x)

$$2 \left(6 x - 1\right)$$

Simplify

The third derivative [src]

$$12$$

Simplify

Gráfico

Derivada y=x^2(2x-1)