Derivative of y=cos4x

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cos(4*x)

$$\cos{\left(4 x \right)}$$

d           
--(cos(4*x))
dx

$$\frac{d}{d x} \cos{\left(4 x \right)}$$

Transform

Detail solution

Let $u = 4 x$ .
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 $\frac{d}{d x} 4 x$ :
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: $4$
The result of the chain rule is:

$- 4 \sin{\left(4 x \right)}$

The answer is:

$- 4 \sin{\left(4 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-4*sin(4*x)

$$- 4 \sin{\left(4 x \right)}$$

Simplify

The second derivative [src]

-16*cos(4*x)

$$- 16 \cos{\left(4 x \right)}$$

Simplify

The third derivative [src]

64*sin(4*x)

$$64 \sin{\left(4 x \right)}$$

Simplify

The graph