How do you differentiate #f(x)= 7xsinx# using the product rule?

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Answer 1 · 2016-02-05T15:21:57

#f'(x) = 7sinx + 7xcosx#

#f(x) = g(x)h(x) -> f'(x) = g'(x)h(x)+g(x)h'(x)#

So for #f(x) = 7xsinx# we can take:

#g(x) = 7x# and #h(x) = sinx#

Thus #g'(x) = 7# and #h'(x) = cosx#

Substituting this into the product rule:

#f'(x) = 7sinx + 7xcosx#