How do you find the derivative of #f(x)= 5 Secx Tanx#?

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Answer 1 · 2017-01-02T11:38:49

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

#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#