The Chain Rule | Derivative of sin(x) with Respect to x is cos(x)

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 is a formula that allows us to differentiate compositions of functions.

In this case, we have the function f(x) = sin(x), where the outer function is sin and the inner function is x.

The chain rule states that if we have a composition of functions f(g(x)), then the derivative of that composition is given by the product of the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

Applying this to our problem, we have:
f(x) = sin(x)
g(x) = x

The derivative of the outer function (sin) is cos(x), and the derivative of the inner function (x) is 1.

Now, we can apply the chain rule:

d/dx(sin(x)) = cos(x) * d/dx(x)

Since d/dx(x) is simply 1, we have:

d/dx(sin(x)) = cos(x) * 1

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

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