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About LinkBacksFor example, the function sin^2(3x^2-2x+12). My text says derive using the chain rule, but isn't this simply two things multiplied together, thus calling for the product rule? Is it the fact that sin is squared that makes the chain rule called for?
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For example, the function sin^2(3x^2-2x+12). My text says derive using the chain rule, but isn't this simply two things multiplied together, thus calling for the product rule? Is it the fact that sin is squared that makes the chain rule called for?
no. it is a function of a function, needing the chaqin rule.
let g(x) = 3x^2-2x+12
then this is sin^2(g(x))whose derivative is 2sin(g(x))cos(g(x))g'(x) =
2sin(g(x))cos(g(x))(6x-2)
plug the quadratic back in for g(x) and you are done.
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