Derivative of y=sin(3x-9)

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sin(3*x - 9)

$$\sin{\left(3 x - 9 \right)}$$

d               
--(sin(3*x - 9))
dx

$$\frac{d}{d x} \sin{\left(3 x - 9 \right)}$$

Transform

Detail solution

Let $u = 3 x - 9$ .
The derivative of sine is cosine:

$\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x - 9\right)$ :
1. Differentiate $3 x - 9$ 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: $3$
  2. The derivative of the constant $\left(-1\right) 9$ is zero.
  The result is: $3$
The result of the chain rule is:

$3 \cos{\left(3 x - 9 \right)}$
Now simplify:

$3 \cos{\left(3 x - 9 \right)}$

The answer is:

$3 \cos{\left(3 x - 9 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

3*cos(3*x - 9)

$$3 \cos{\left(3 x - 9 \right)}$$

Simplify

The second derivative [src]

-9*sin(3*(-3 + x))

$$- 9 \sin{\left(3 \left(x - 3\right) \right)}$$

Simplify

The third derivative [src]

-27*cos(3*(-3 + x))

$$- 27 \cos{\left(3 \left(x - 3\right) \right)}$$

Simplify

The graph