Question

What is the derivative of `y=tansqrt(2x+5)`?

Answer 1

`sec^2(sqrt(2x+5))/sqrt(2x+5)`

Explanation:

First substitute `t = sqrt(2x+5) = (2x+5)^(1/2)`
Then `y = tan(t)`
`dy/dt = sec^2(t)`
`dt/dx = 1/2(2x+5)^(-1/2)*2 = 1/sqrt(2x+5)`
`dy/dx = dy/dt*dt/dx = sec^2(sqrt(2x+5))/sqrt(2x+5)`