Finding the Derivative of Cos(x) Using the Chain Rule: Step-by-Step Guide and Explanation

Derivative of cosx

The derivative of cos(x) can be found using the chain rule

The derivative of cos(x) can be found using the chain rule. The chain rule states that if we have a composite function, such as f(g(x)), then the derivative of this function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

In this case, we have f(x) = cos(x), which is the outer function, and g(x) = x, which is the inner function. So, we can use the chain rule to find the derivative of f(g(x)) = cos(x).

The derivative of f(g(x)) with respect to x is given by:

(d/dx) [cos(g(x))] = -sin(g(x)) * g'(x)

Here, g'(x) represents the derivative of g(x), which is equal to 1.

So, substituting g(x) = x and g'(x) = 1 into the formula, we get:

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

Thus, the derivative of cos(x) is equal to -sin(x).

Therefore, d/dx[cos(x)] = -sin(x).

More Answers:

Derivative of arccos(x) with Respect to x: Step-by-Step Guide and Calculation
Master the Differentiation of Arctan(x) with the Chain Rule: Derivative of Arctan(x) Unveiled
Derivative of sin(x): Understanding and Applying the Chain Rule in Differentiation

Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded

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 »