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Here we have a product of two things, so we will be using the product rule of differentiation. This is: for y=u(x)v(x), where u(x) and v(x) are funtions of x, dy/dx = u'(x)v(x) + u(x)v'(x). So in this ...

We can't integrate cos^2(x) as it is, so we want to change it into another form. We can easily do this using trig identities.

1) Recall the double angle formula:

c...

There's a nice trick here you can do, treat the equation as 1*ln(x) then intergrate by parts.

Differentiating ln(x) gives 1/x, while intergrating 1 gives x

So your left with...

First off, an explicit definition needs to be understood. An explicit definition is the standard form in which many equations are found:

y = f(x)        (1)

for example:  y=...

Often, it can seem daunting when you are asked to differentiate a function that looks particularly messy. However, it's really quite simple if you break it down in easy to manage steps....