What is the derivative of x 2sinx

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 Mathematics section.

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

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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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