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

1 Answer
Roella W.
Jan 8, 2016

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)

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