# What is the derivative of x 2sinx

## Sin x derivative The derivative of the sine function is the cosine function. We'll go into that again 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:

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### 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 must 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, one must consider the following things:

1. tan x is equivalent to sin x divided by cos x.
2. You have to know how the quotient rule works: read the quotient rule
3. Trigonometric Pythagoras: sin2 a + cos2 a = 1

Invoice: Example 4: sinx x

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

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