How do you differentiate #f(x)=3secx(tanx)#?

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Answer 1 · 2017-11-01T08:39:13

#f'(x)=3secx(tan^2x+sec^2x)#

we need to use the product rule for this function

#f(x)=u(x)v(x)#

#=>f'(x)=v(x)color(red)(u'(x))+u(x)color(blue)(v'(x))#

so

#f(x)=3secxtanx#

#=>f'(x)=d/(dx)(3secxtanx)#

#f'(x)=3tanxcolor(red)(d/(dx)(secx))+3secxcolor(blue)(d/(dx)(tanx))#

#f'(x)=3tanxcolor(red)(secxtanx)+3secxcolor(blue)(sec^2x)#

#f'(x)=3secxtan^2x+3sec^3x#

#f'(x)=3secx(tan^2x+sec^2x)#