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

1 Answer
Nov 1, 2017

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

Explanation:

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)