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

(d/dx) sinx =

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

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

The chain rule states that if we have a composition of functions where y = f(g(x)), then the derivative of y with respect to x is given by (dy/dx) = (dy/dg) * (dg/dx).

In the case of sin(x), we can think of it as the composition of two functions: y = f(g(x)) = sin(x), where g(x) = x.

The derivative of sin(x) with respect to x can be found by differentiating each part of the composition separately.

First, we differentiate the outer function f(g(x)), which is sin(x). The derivative of sin(x) with respect to x is cos(x).

Second, we differentiate the inner function g(x), which is simply x. The derivative of x with respect to x is 1.

Using the chain rule, we multiply the derivatives:
(dy/dx) = (dy/dg) * (dg/dx) = cos(x) * 1 = cos(x).

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

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