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:

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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 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:

  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

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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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