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If y= (5x)/(1-x^2)^(1/3) + sin^2(2x+3) ....

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

Text Solution

Verified by Experts

We have
`y=5x(1-x^(2))^(-1//3)+sin^(2)(2x+3)`
`rArr" "(dy)/(dx)=(d)/(dx){5x(1-x^(2))^(-1//3)}+(d)/(dx){sin^(2)(2x+3)}`
`={5x.((-1)/(3))(1-x^(2))^(-4//3).(-2x)+(1-x^(2))^(-1//3)*5}+{2sin(2x+3)cos(2x+3).2}`
`=(10x^(2))/(3(1-x^(2))^(4//3))+(5)/((1-x^(2))^(1//3))+2sin(4x+6)`
`=(10x^(2)+15(1-x^(2)))/(3(1-x^(2))^(4//3))+2sin(4x+6)`
`=((15-5x^(2)))/(3(1-x^(2))^(4//3))+2 sin (4x+6)`.
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