Question

What is the derivative of `3sec^2x + tan^2x`?

Answer 1

`8sec^2(x)tan(x)`

Explanation:

Use partial differentiation.
Looking at the first term, let `sec(x) = t`
Then `d/dt 3t^2 = 6t`
`d/dx sec(x) = sec(x)tan(x)`
`d/dt*d/dx = 6sec(x)sec(x)tan(x) = 6sec^2(x)tan(x)`

for the second term, let `tan(x) = t`
`d/dt t^2 = 2t`
`d/dx tan(x) = sec^2(x)`
`d/dt*d/dx = 2tan(x)sec^2(x)`

Then the whole derivative is
`6sec^2(x)tan(x) + 2sec^2(x)tan(x)`
`=8sec^2(x)tan(x)`