# What is 6cos x 3 differentiated

## Sin x derivative

**We will deal with the derivation of sin x in this article. We also provide you with a number of examples relating to the derivation of sin x. This article is part of our math section.**

The derivative of the sine function is the cosine function. We'll go back to that in a moment. Before doing this, however, you should take a look at the following derivation rules. These are needed to understand examples of derivation:

Show:**Sin x derivatives examples**

In the following we will deal with the derivation of the sine function as well as some functions that also have to do with sine.

**Example 1: sin x**

Basically, if you derive the sine function, you get the cosine function.

**Example 2: ****y = 2 **·** sin (3x)**

The derivation of the function y = 2 · sin (3x) is to be formed. To do this, we have to rely on the use of the chain rule.

**y = 2**·**sin (3x)**- Substitution: u = 3x
- Outer function = 2 sin (u)
- Outer derivative = 2 cos (u)
- Inner function = 3x
- Inner derivative = 3
- y '= 3 2 cos (u)
- y '= 6 cos (3x)

**Example 3: tan x**

Example 3 is about the derivation of tan x. To do this, you have to pay attention to the following things:

- tan x is equivalent to sin x divided by cos x.
- You have to know how the quotient rule works: read the quotient rule
- Trigonometric Pythagoras: sin
^{2}a + cos^{2 }a = 1

Invoice:

**Example 4: sinx x**

In this example we want to derive sin x · x. We use the product rule for this.

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