The Chain Rule: Finding the Derivative of sin(x) with Respect to x and Its Application

d/dx [sinx]

To find the derivative of the function f(x) = sin(x) with respect to x, denoted by d/dx [sin(x)], we can use the chain rule

To find the derivative of the function f(x) = sin(x) with respect to x, denoted by d/dx [sin(x)], we can use the chain rule.

The chain rule states that if we have a composite function f(g(x)), then the derivative of f(g(x)) with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

In this case, f(x) = sin(x), so we can consider f as the outer function and g(x) = x as the inner function.

First, let’s find the derivative of the inner function g(x) = x, which is simply 1.

Next, let’s find the derivative of the outer function f(g(x)) = sin(x). The derivative of sin(x) with respect to x is cos(x).

Now, using the chain rule, we multiply the derivative of the outer function by the derivative of the inner function:

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

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

More Answers: