How to Find the Derivative of sin(x) with Respect to x | Step-by-Step Guide

d/dx sin(x)

To find the derivative of sin(x) with respect to x, we can use the basic differentiation rules

To find the derivative of sin(x) with respect to x, we can use the basic differentiation rules.

The derivative of sin(x) is calculated using the chain rule, which states that if we have a composite function, such as sin(x), we need to differentiate the outer function (in this case, sin) and multiply it by the derivative of the inner function (in this case, x).

So, let’s differentiate sin(x) step by step:

Step 1: Identify the outer function and the inner function.
In this case, the outer function is sin(x), and the inner function is x.

Step 2: Differentiate the outer function.
The derivative of sin(x) is cos(x). This is a well-known and fundamental result in calculus.

Step 3: Multiply by the derivative of the inner function.
The derivative of x with respect to x is simply 1.

Step 4: Combine the results.
Multiply the derivative of the outer function, cos(x), by the derivative of the inner function, which is 1. This gives us:

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

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

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

More Answers: