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IceColdCola19
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How would I do the derivative of
f(x) = cos pi*x
I know f'(x) cos x = - sin x but what about that pi?
f(x) = cos pi*x
I know f'(x) cos x = - sin x but what about that pi?
The derivative of f(x) = cos pi*x is -pi*sin pi*x.
This is because the derivative of cos x is -sin x, and the chain rule applies when taking the derivative of a function with a constant multiplied by the input. In this case, the constant is pi.
No, the derivative of f(x) = cos pi*x is negative when x is an odd multiple of pi/2, and positive when x is an even multiple of pi/2.
The graph of f(x) = cos pi*x is a cosine wave, while the graph of its derivative, -pi*sin pi*x, is a sine wave. The derivative graph will have a peak or trough at the same points where the original function has a zero or maximum/minimum.
Yes, the derivative of a function gives the slope of the tangent line at that point. In the case of f(x) = cos pi*x, the derivative at a specific point x will give the slope of the tangent line at that point on the cosine wave.