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First step is to understand all the notation, i.e. the prime for derivative. We then need to understand that the derivative is the gradient of the tangent at a point. In this case at the point P we can fi...

A sonata form is a musical structure that originated from a ternary form (a three part form); coming into recognition in the early Classical era. Despite variations in the form, the general form consists ...

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))'...