How to Find the Derivative of Cos(x) Using the Chain Rule: Step-by-Step Guide

d/dx(cosx)

sinx

To find the derivative of cos(x) with respect to x, we can use the chain rule. The chain rule states that if we have a function f(g(x)), then the derivative is f'(g(x)) * g'(x).

In this case, our function is cos(x), so g(x) = x. Thus, we have f(g(x)) = cos(x) and g(x) = x.

Now, we need to find the derivative of cos(x) with respect to x using the chain rule:

f'(g(x)) = -sin(g(x)) = -sin(x)

g'(x) = 1

So, putting it all together, we have:

d/dx(cos(x)) = f'(g(x)) * g'(x) = -sin(x) * 1 = -sin(x)

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

More Answers:
Mastering Set-Builder Notation: A Comprehensive Guide to Defining Sets
How to Find the Derivative of Cot(x) using the Quotient Rule: A Comprehensive Guide
Mastering Derivative of Tangent Function: The Quotient Rule Made Easy

Share:

Recent Posts

Mathematics in Cancer Treatment

How Mathematics is Transforming Cancer Treatment Mathematics plays an increasingly vital role in the fight against cancer mesothelioma. From optimizing drug delivery systems to personalizing

Read More »