How to Find the Derivative of sin(x) using the Chain Rule

Dx {sin x}=?

To find the derivative of the function f(x) = sin(x), we can use the basic derivative rules

To find the derivative of the function f(x) = sin(x), we can use the basic derivative rules. In this case, we will need to use the chain rule since the function is composed with the sine function.

The chain rule states that if we have a composition of functions f(g(x)), then the derivative of the composition is given by:

(f(g(x)))’ = f'(g(x)) * g'(x)

In our case, f(x) = sin(x) and g(x) = x. So, let’s find the derivatives of the components:

The derivative of f(x) = sin(x) with respect to x is given by:

f'(x) = cos(x)

The derivative of g(x) = x with respect to x is simply:

g'(x) = 1

Now applying the chain rule by multiplying f'(g(x)) with g'(x):

(f(g(x)))’ = f'(g(x)) * g'(x)
= cos(x) * 1
= cos(x)

Therefore, the derivative of f(x) = sin(x) is:

f'(x) = cos(x)

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