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

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

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Answer 1 · 2016-01-08T11:12:00

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

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