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

d/dx(sinx)

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

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

The chain rule states that if we have a composite function y = f(g(x)), where g(x) is differentiable at x and f(u) is differentiable at u = g(x), then the derivative of y with respect to x is given by dy/dx = f'(g(x)) * g'(x).

In this case, f(u) = sin(u) and g(x) = x. So we have y = f(g(x)) = sin(x).

To differentiate sin(x), we need to find the derivatives of sin(u) with respect to u (which is cos(u)) and differentiate g(x) with respect to x (which is 1).

Therefore, using the chain rule, dy/dx = f'(g(x)) * g'(x) = cos(g(x)) * 1 = cos(x).

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

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Mastering Differentiation: The Power, Product, Quotient, and Chain Rules for Calculating Derivatives

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