How do you differentiate # f(x) =2xcos xtanx #?

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Answer 1 · 2017-01-22T16:03:02

#f'(x) = 2(sinx + xcosx)#

Rewrite #tanx# as #sinx/cosx#:

#f(x) = 2xcosx(sinx/cosx)#

#f(x) = 2xsinx#

Differentiate using the product rule. Let #f(x) = g(x) * h(x)#, with#g(x) = 2x# and #h(x) =sinx#. Then #g'(x) = 2# and #h'(x) = cosx#.

The product rule states that #f'(x) = g'(x)h(x) + h'(x)g(x)#.

#f'(x) = 2sinx + 2xcosx#

#f'(x) = 2(sinx + xcosx)#

Hopefully this helps!