` ` Q. If `y =` `(5x) / root(3) ( 1 - x^2)` `+` `sin^2(2x + 3)` . Find `dy/dx` .

Expert Answers

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Given `y=(5x)/root(3)(1-x^2)+sin^2(2x+3)` we are asked to find `(dy)/(dx)` :

Rewrite as `y=5x(1-x^2)^(-1/3)+sin^2(2x+3)`

Use the product rule and the chain rule on the first term, and use the chain rule twice on the second term:





Factor out the common factor of `5(1-x^2)^(-4/3)` from the first two terms and use the double angle identity on the last term:



or `(dy)/(dx)=-(5(x^2-3))/(3(1-x^2)^(4/3))+2sin(4x+6)`


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