How do you differentiate #f(x)=(x^2+4x)*secx# using the product rule?

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Answer 1 · 2015-12-20T06:21:40

#f'(x)=(2x+4)secx+(x^2+4x)secxtanx#

According to the product rule:

#f'(x)=secxd/dx[x^2+4x]+(x^2+4x)d/dx[secx]#

Find each derivative independently.

#d/dx[x^2+4x]=2x+4#

#d/dx[secx]=secxtanx#

Plug these values back in.

#f'(x)=secx(2x+4)+secxtanx(x^2+4x)#

If you wish to factor:

#f'(x)=secx(2(x+2)+x(x+4)tanx)#