Calculus
Evaluate f′(x)f^{\(\prime\)}\(\left\)(x\(\right\)) at x=π4x=\(\frac{\pi}{4}\) if f(x)=cosxf\(\left\)(x\(\right\))=\(\cos\) x.
A wave travels along a string, and its position in millimeters is described by h(t)=15(2cost+1)h\(\left\)(t\(\right\))=15\(\left\)(2\(\cos\) t+1\(\right\)), for t≥0t\(\geq\)0, where tt represents time in seconds. Determine the velocity of the wave, v(t)=h′(t)v\(\left\)(t\(\right\))=h^{\(\prime\)}\(\left\)(t\(\right\)).
Consider the equation below. Using differentiation, state if it is true or false.
ddx(2cotxcsc2x−8cotx−6x)=−6cot4x\(\frac{d}{dx}\]\left\)(2\(\cot\) x\(\csc\)^2x-8\(\cot\) x-6x\(\right\))=-6\(\cot\)^4x
