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Find the derivative of f(x)\, with respect to x\,: f(x)=\sin ^{2}(7x+5)+\cos ^{2}(7x+5)\,

One way to find this derivative is to take the derivative of each part and do some arithmetic. However, the easiest way is to remember the trig identity which tells us that \sin ^{2}x+\cos ^{2}x=1\, for all x\,. Thus we have

f(x)=\sin ^{2}(7x+5)+\cos ^{2}(7x+5)=1\,



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