Derivative of sin(5*x)

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sin(5*x)

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

sin(5*x)

Detail solution

Let $u = 5 x$ .
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 $\frac{d}{d x} 5 x$ :
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:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

5*cos(5*x)

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

Simplify

The second derivative [src]

-25*sin(5*x)

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

Simplify

The third derivative [src]

-125*cos(5*x)

$$- 125 \cos{\left(5 x \right)}$$

Simplify

The graph