Derivative of sin(x): Understanding and Applying the Chain Rule in Differentiation

Derivitave of sinx

The derivative of sin(x) can be found by applying the basic rules of differentiation

The derivative of sin(x) can be found by applying the basic rules of differentiation. To differentiate sin(x), we use the chain rule.

Let’s start with the definition of the sine function: sin(x) = opp/hyp, where opp is the length of the side opposite to angle x in a right triangle, and hyp is the length of the hypotenuse.

Now, let’s find the derivative.

We can rewrite sin(x) as y = sin(x), where y represents the dependent variable and x represents the independent variable.

Using the chain rule, we have:

dy/dx = d/dx[sin(x)]

To differentiate sin(x) with respect to x, we need to multiply the derivative of the outer function (sin) with the derivative of the inner function (x).

The derivative of sin(x) is given by the derivative of its outer function cosine (cos) multiplied by the derivative of the inner function:

dy/dx = cos(x) * d/dx[x]

Now, the derivative of x with respect to x is simply 1:

dy/dx = cos(x)

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

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