Understanding the Chain Rule: Derivative of sin(x) with Respect to x is cos(x)

d/dx [sin x]

To find the derivative of the function f(x) = sin(x) with respect to x, we can use the chain rule

To find the derivative of the function f(x) = sin(x) with respect to x, we can use the chain rule.

The chain rule states that if we have a composite function g(f(x)), where g(x) and f(x) are both differentiable, then the derivative of g(f(x)) with respect to x is given by g'(f(x)) * f'(x).

In this case, our composite function is sin(x). We need to find the derivative of sin(x) with respect to x.

The derivative of sin(x) is given by:

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

So, the derivative of the function f(x) = sin(x) with respect to x is f'(x) = cos(x).

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

To summarize, the derivative of sin(x) with respect to x is cos(x).

More Answers:

Understanding Rolle’s Theorem: A Fundamental Theorem in Calculus Explaining the Existence of Points with Zero Derivative
Understanding Local Minimums: Evaluating the Behavior of a Function around a Point
Understanding Critical Numbers: Examining the Relationship between Concavity and Extremes

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