Finding the Derivative of sin(x) with Respect to x Using the Chain Rule

d/dx sinx

The derivative of sin(x) with respect to x, denoted as d/dx (sinx), can be found using the chain rule of derivatives

The derivative of sin(x) with respect to x, denoted as d/dx (sinx), can be found using the chain rule of derivatives. The chain rule states that if y = f(g(x)), then the derivative of y with respect to x is given by the product of the derivative of f(g(x)) with respect to g(x) and the derivative of g(x) with respect to x.

In this case, sin(x) can be thought of as f(g(x)), where g(x) = x and f(x) = sin(x). Therefore, the derivative of sin(x) with respect to x can be found as follows:

Let y = sin(x)
Let u = x

We can rewrite sin(x) as y = f(u) = sin(u)

Now, we will calculate the derivative of f(u) = sin(u) with respect to u, which is denoted as df/du.

df/du = cos(u)
= cos(x)

Next, we will calculate the derivative of u = x with respect to x, which is denoted as du/dx.

du/dx = 1

Finally, we can apply the chain rule:

d/dx (sinx) = (df/du) * (du/dx)
= cos(x) * 1
= cos(x)

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

More Answers: