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Geysers are intermittent discharges of turbulent water from the Earth's surface. One of the most famous examples is Old Faithful in Yellowstone National Park, North America.

There are several facto...

a)   f'(x)=uv'+vu'     if    f(x)= uv

u=2x  u'=2  v=sin(x)   v'=cos(x)

g'(x)=2x cos(x) +2sin(x)

b)   g'(π) = 2π cos(π)+2sin(π)  = 2 π (-1) + 2 (0)

      g'(π) = -2π

The product rule states (assuming x' is the differential of x): (fg)​′​​=f​′​​g+fg​′​​ Substitute the values into the rule: (sin(x)cos(x))' = sin(x)'cos(x) + sin(x)cos(x)' (sin(x)cos(x))'...

For all straight line equations as the one above, the equation is y=mx+c where: m is the gradient, c is the y-intercept. Thus from the arrangement of the given equation, gradient ...