Understanding the Derivative of the Sine Function | How the Value of Sine Changes with Respect to x

d/dx[sin(x)]

The derivative of the sine function, denoted as d/dx[sin(x)], represents how the value of sine changes with respect to the independent variable x

The derivative of the sine function, denoted as d/dx[sin(x)], represents how the value of sine changes with respect to the independent variable x. To find this derivative, we can use the rules of differentiation and apply them to the sine function.

The derivative of sine is found by differentiating it as if it were a composite function. Recall that the derivative of a composite function can be calculated using the chain rule:

If we have a composite function f(g(x)), the derivative of f(g(x)) with respect to x is given by d/dx[f(g(x))] = f'(g(x)) * g'(x).

In our case, f(x) is the sine function, and x is our variable. Therefore, g(x) = x.

Now, let’s differentiate the sine function with respect to x:

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

So, the derivative of the sine function with respect to x is simply the cosine of x, written as cos(x).

This means that at any particular point on the sine curve, the rate of change of the function is given by the cosine function.

More Answers:
The Chain Rule | Finding the Derivative of cos(x) with Respect to x
How to Find the Derivative of the Tangent Function with the Chain Rule and Express It as sec^2(x)
Exploring the Chain Rule | Finding the Derivative of e^x with Respect to x

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