You can consider this function as follows:
Then,
Just as the equation:
becomes:
Ignorant question here, but I was looking at this example i have, needing to take the derivative:
f'(x) = sin^2(x) + cos(x)
= 2sin(x)*d/dx(sin x) - sin(x)
= 2sin(x)*cos(x) - sin(x)
and so on... I'm wanting to know why the 2sin(x) isn't where the differentiation stops for sin^2(x)? there's the 2sin(x), and then the d/dx(sinx) added in as well. The cos(x) on the right side doesn't have any extra steps for it. Hope this makes sense, and i realize this is a silly question but I just wanted the clarification.
Because it's not true that [LaTeX ERROR: Convert failed] . In general, [LaTeX ERROR: Convert failed] unless [LaTeX ERROR: Convert failed] The derivative of f at x is defined as the limit [LaTeX ERROR: Convert failed] , but unfortunately, many students (at school, anyway) understand it as [LaTeX ERROR: Convert failed] . The power rule is itself as a result of considering the function [LaTeX ERROR: Convert failed] at [LaTeX ERROR: Convert failed] , and using the definition of the derivative to calculate [LaTeX ERROR: Convert failed] as [LaTeX ERROR: Convert failed] . If I were to ever teach (school) calculus, it's one of those things I would write in giant letters somewhere above the board.