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Higher-order Derivatives
The first derivative is the slope of a curve, and the second derivative is the slope of the slope, like acceleration. So what's the third derivative? (Fun fact: it's actually called jerk.)
What is the fewest number of derivatives one needs to compute so that \(f(x) = 568{ x }^{ 499 }\) becomes zero?
by
Merzel Mark Guilaran
by
Gene Keun Chung
by
Gene Keun Chung
Let \(P\) be a point moving in the \(xy\)-plane whose coordinates at time \(t\) are given by \[x(t)=2e^t\sin t, y(t)=6\cos t.\] What is the minimum value of the magnitude of the acceleration of \(P?\)
by
Arron Kau
Find \(f^{(100)}(0)\). If
\[\large{ f(x) = \sin x + x^{100000}}\]
Note: \(f^n(x)\) denotes the \(n^{th}\) derivative of \(f(x)\).
by
Paul Ryan Longhas