Derivative of cos(9*x)

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cos(9*x)

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

cos(9*x)

Detail solution

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-9*sin(9*x)

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

Simplify

The second derivative [src]

-81*cos(9*x)

$$- 81 \cos{\left(9 x \right)}$$

Simplify

The third derivative [src]

729*sin(9*x)

$$729 \sin{\left(9 x \right)}$$

Simplify

The graph