How do you use the product Rule to find the derivative of #(2x)(-sinx) + (cosx)(2) - 2(cosx)#?

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Answer 1 · 2015-08-11T23:28:40

First of all, notice how this cancels to give:

#(2x)(-sinx)#

Much easier now. Using the product rule, you have:

#f(x) = g(x)h(x)#

#(df)/(dx) = g(x)(dh)/(dx) + h(x)(dg)/(dx)#

So, you get:

#= (2x)*d/(dx)[-sinx] + (-sinx)*d/(dx)[2x]#

#= (2x)*(-cosx) + (-sinx)*2#

#= color(blue)(-2xcosx - 2sinx)#