Derivative of y=cos5x

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cos(5*x)

$$\cos{\left(5 x \right)}$$

d           
--(cos(5*x))
dx

$$\frac{d}{d x} \cos{\left(5 x \right)}$$

Transform

Detail solution

Let $u = 5 x$ .
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 $\frac{d}{d x} 5 x$ :
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: $5$
The result of the chain rule is:

$- 5 \sin{\left(5 x \right)}$

The answer is:

$- 5 \sin{\left(5 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-5*sin(5*x)

$$- 5 \sin{\left(5 x \right)}$$

Simplify

The second derivative [src]

-25*cos(5*x)

$$- 25 \cos{\left(5 x \right)}$$

Simplify

The third derivative [src]

125*sin(5*x)

$$125 \sin{\left(5 x \right)}$$

Simplify

The graph