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Derivative of:
Derivative of 4^(2*x)
Derivative of x^-9
Derivative of -x^4
Derivative of y=1/2sin2x
Graphing y =:
4*(x-2)^2-5
Identical expressions
four *(x- two)^ two - five
4 multiply by (x minus 2) squared minus 5
four multiply by (x minus two) to the power of two minus five
4*(x-2)2-5
4*x-22-5
4*(x-2)²-5
4*(x-2) to the power of 2-5
4(x-2)^2-5
4(x-2)2-5
4x-22-5
4x-2^2-5
Similar expressions
4*(x+2)^2-5
4*(x-2)^2+5

The derivative of the function/ 4*(x-2)^2-5

Derivative of 4*(x-2)^2-5

The solution

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         2    
4*(x - 2)  - 5

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

4*(x - 2)^2 - 5

Detail solution

Differentiate $4 \left(x - 2\right)^{2} - 5$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = x - 2$ .
  2. Apply the power rule: $u^{2}$ goes to $2 u$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 2\right)$ :
    1. Differentiate $x - 2$ term by term:
      1. Apply the power rule: $x$ goes to $1$
      2. The derivative of the constant $-2$ is zero.
      The result is: $1$
    The result of the chain rule is:
    
    $2 x - 4$
  So, the result is: $8 x - 16$
2. The derivative of the constant $-5$ is zero.
The result is: $8 x - 16$

The answer is:

$8 x - 16$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-16 + 8*x

$$8 x - 16$$

Simplify

The second derivative [src]

$$8$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of 4*(x-2)^2-5