How do you differentiate #f(x)=x^3*sec2x# using the product rule?

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Answer 1 · 2015-12-01T15:59:17

#f'(x)=x^2sec2x(3+2xtan2x)#

According to the product rule:

#f'(x)=sec2xd/dx[x^3]+x^3d/dx[sec2x]#

Calculate both derivatives.

#d/dx[x^3]=3x^2#

#d/dx[sec2x]=sec2xtan2x*d/dx[2x]=2sec2xtan2x#

Plug these back in:

#f'(x)=3x^2sec2x+2x^3sec2xtan2x#

If you feel like factoring:

#f'(x)=x^2sec2x(3+2xtan2x)#