A Beginner’s Guide | Understanding the Derivative of sin(x) Using the Chain Rule

d/dx(sinx)

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

To find the derivative of the function f(x) = sin(x), we can use the chain rule. The chain rule is applied when we have a composition of functions. In this case, we have the function sin(x) nested inside the function f(x).

Using the chain rule, the derivative of f(x) = sin(x) can be found as follows:

1. Let u = sin(x), then f(x) = u.
2. Find the derivative of u with respect to x, which is du/dx = cos(x).
3. Now, using the chain rule, we have: d/dx[f(x)] = d/du[u] * du/dx.
Substituting the corresponding values, we get: d/dx(sin(x)) = d/du[u] * du/dx = cos(x) * 1 = cos(x).

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

In summary, d/dx(sin(x)) = cos(x).

More Answers: