How do you find the derivative of #y=10tan(20x)#?

1 Answer
Jul 2, 2016

#dy/dx=200sec^2(20)x#

Explanation:

First we need to find the derivative of #Tan ax# where a is constant
#y = tanax#
#dy/dx=d/dx((sinax)/(cosax))#
applying #u/v# rule
where #u=sinax,v=cosax#
#dy/dx#=#(1/(cos^2ax))##(cosax##(d/dx(sinax))#-#sinax(d/dx(cosax))#
#dy/dx#=#(1/(cos^2ax))#*#(cosax*acosx)#-#sinax*(-asinax))#
#dy/dx#=#a(sin^2ax+cos^2ax)/(cos^2ax)#=#a/(cos^2ax)#
#dy/dx#=#asec^2ax#
so as in the problem y = 10 tan 20x
the answer is #dy/dx=10*20*sec^2(10x)=200sec^2(20x)#