JEE Advance - Mathematics (1981 - No. 21)
Let $$y = {e^{x\,\sin \,{x^3}}} + {\left( {\tan x} \right)^x}$$. Find $${{dy} \over {dx}}$$
${e^{x\,\sin {x^3}}}\left[ {\sin {x^3} + 3{x^3}\cos {x^3}} \right] + {\left( {\tan x} \right)^x}\left[ {\sec^2 x + \log \,\tan x} \right]$
${e^{x\,\sin {x^3}}}\left[ {\sin {x^3} + x\cos {x^3}} \right] + {\left( {\tan x} \right)^x}\left[ {x\sec^2 x + \log \,\tan x} \right]$
${e^{x\,\sin {x^3}}}\left[ {\sin {x^3} + 3{x^3}\cos {x^3}} \right] + {\left( {\tan x} \right)^x}\left[ {{{x\sec^2 x} \over {\tan x}} + \log \,\tan x} \right]$
${e^{x\,\sin {x^3}}}\left[ {\sin {x^3} + 3{x^2}\cos {x^3}} \right] + {\left( {\tan x} \right)^x}\left[ {{{x\sec^2 x} \over {\tan x}} + \log \,\tan x} \right]$
${e^{x\,\sin {x^3}}}\left[ {\sin {x^3} + 3{x^3}\cos {x^3}} \right] + {\left( {\tan x} \right)^x}\left[ {{{x\sec^2 x} } + \log \,\tan x} \right]$