Proof: Derivative of sin(x) = cos(x) by First Principles

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In this video, we prove that the derivative of sin(x) equals cos(x) by the very definition of the derivative, which is:

df/dx = f'(x) = lim_(h approaches 0) f(x + h) - f(x) / h

Thus:

d/dx [sin(x)] = lim_(h approaches 0) sin(x + h) - sin(x) / h

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You do a great service for calculus students by illustrating the simple idea behind derivatives, especially the visualization of trigonometric derivatives.

garyward
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Holy shit, never thought about the slopes like that. Awesome stuff

ankushsarkar