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Find the differential of y(x)=(5x*Cos(3x))^2

Firstly I would state the substitution rule, letting 5xCos(3x)=w(x), and differentiating with respect to w(x). This gives y'(x)=2w'(x)(w(x)).I would then demonstrate the product rule stating where u and v are functions of x. That (uv)'=v'u+vu'. And apply this to the example giving w'(x)=5Cos(3x)-15xSin(3x).substituting w(x) and w'(x) back into the equation gives y'(x)=(10Cos(3x)-30xSin(3x))5xCos(3x)

Answered by Harry L. • Maths tutor

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