Derivative of sin x

Step by step

The question

Question: find the derivative of f(x) = sin x.

1 The rules

The derivative of sin x is cos x.

2 Each term

Use the rule on each term.

3 Tidy up

So f′(x) = cos x.

4 Check

Let's check: the derivative is the slope.

At x = 1, the rule gives 0.5403, with a calculator in radians.

Now the slope between two very close points: x = 1 and x = 1.001.

A calculator gives about 0.54.

Very close to 0.5403.

Right!

Let's look back.

First: the rules.

Then: each term.

Then: tidy up.

Last: check.