How do you find the derivative of f(x)= 5 Secx Tanxf(x)=5secxtanx?

1 Answer
Jan 2, 2017

f'(x)=10secxtan^2x+5secx

Explanation:

use the product rule

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

f(x)=color(red)(5secx)color(blue)(tanx)

color(red)(u=5secx=>u'=5secxtanx

color(blue)(v=tanx=>v'=sec^2x

:.f'(x)=color(blue)(tanx)color(red)(5secxtanx)+color(red)(5secx)color(blue)(sec^2x

f'(x)=5secxtan^2x+5sec^3x

f'(x)=5secx(tan^2x+sec^2x)

f'(x)=5secx(tan^2x+1+tan^2x))

f'(x)=5secx(2tan^2x+1)=10secxtan^2x+5secx