Derivative of sine function – Step-by-step guide with the chain rule

(d/dx) sin(x)

To find the derivative of sin(x) with respect to x, we can apply the chain rule

To find the derivative of sin(x) with respect to x, we can apply the chain rule. The chain rule states that if we have a function f(g(x)), then the derivative of f(g(x)) with respect to x is given by f'(g(x)) * g'(x).

In this case, f(x) = sin(x) and g(x) = x. So, we need to find the derivatives of f(x) and g(x) and then multiply them using the chain rule.

The derivative of f(x) = sin(x) is found using the standard derivative of sin(x), which is cos(x).

The derivative of g(x) = x is simply 1, as the derivative of x with respect to x is 1.

Now, applying the chain rule, the derivative of sin(x) with respect to x is:

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

Therefore, the derivative of sin(x) with respect to x is cos(x).

To summarize:
(d/dx) sin(x) = cos(x).

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