Let y = 4e^tanx . Find dy/dx

asked Feb 13, 2020 66.9k views

4 votes

by Sire

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5 votes

$y=4e^(\tan x)$

$(\mathrm dy)/(\mathrm dx)=(\mathrm d)/(\mathrm dx)[4e^(\tan x)]$

Factor out the constant:

$(\mathrm dy)/(\mathrm dx)=4(\mathrm d)/(\mathrm dx)[e^(\tan x)]$

Apply the chain rule:

$(\mathrm dy)/(\mathrm dx)=4e^(\tan x)(\mathrm d)/(\mathrm dx)[\tan x]$

Wrap it up:

$(\mathrm dy)/(\mathrm dx)=4e^(\tan x)\sec^2x$

Idongesit answered Feb 18, 2020

5.5k points

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