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Derivative of:
Derivative of sqrt(x^3)
Derivative of sqrt(x^2)
Derivative of atan(1/x)
Derivative of 6^x
Graphing y =:
(2*x-3)^2
Canonical form:
(2*x-3)^2
Identical expressions
(two *x- three)^ two
(2 multiply by x minus 3) squared
(two multiply by x minus three) to the power of two
(2*x-3)2
2*x-32
(2*x-3)²
(2*x-3) to the power of 2
(2x-3)^2
(2x-3)2
2x-32
2x-3^2
Similar expressions
(2*x+3)^2

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

Derivative of (2*x-3)^2

The solution

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         2
(2*x - 3)

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

(2*x - 3)^2

Detail solution

Let $u = 2 x - 3$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x - 3\right)$ :
1. Differentiate $2 x - 3$ 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 $-3$ is zero.
  The result is: $2$
The result of the chain rule is:

$8 x - 12$

The answer is:

$8 x - 12$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-12 + 8*x

$$8 x - 12$$

Simplify

The second derivative [src]

$$8$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of (2*x-3)^2