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Derivative of:
Derivative of x/(2*x-1)
Derivative of (x^2+1)/(x^2-1)
Derivative of x^2+4
Derivative of (x^2-1)^3
Identical expressions
three *(two *x- one)^ two
3 multiply by (2 multiply by x minus 1) squared
three multiply by (two multiply by x minus one) to the power of two
3*(2*x-1)2
3*2*x-12
3*(2*x-1)²
3*(2*x-1) to the power of 2
3(2x-1)^2
3(2x-1)2
32x-12
32x-1^2
Similar expressions
3*(2*x+1)^2

The derivative of the function/ 3*(2*x-1)^2

Derivative of 3(2x-1)^2

The solution

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           2
3*(2*x - 1)

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

d /           2\
--\3*(2*x - 1) /
dx

\frac{d}{d x} 3 \left(2 x - 1\right)^{2}

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 2 x - 1$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x - 1\right)$ :
  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 $\left(-1\right) 1$ is zero.
    The result is: $2$
  The result of the chain rule is:
  
  $8 x - 4$
So, the result is: $24 x - 12$

The answer is:

24 x - 12

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-12 + 24*x

24 x - 12

Simplify

The second derivative [src]

24

Simplify

The third derivative [src]

0

Simplify

The graph

Derivative of 3*(2*x-1)^2