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given y=(5x)/(3*sqrt(1-x)^2)+cos^2(2x+1)...

given `y=(5x)/(3*sqrt(1-x)^2)+cos^2(2x+1)`,find `dy/dx`

Text Solution

Verified by Experts

The correct Answer is:
`{{:(5/(3(1-x)^(2)) -2 sin (4x+2)"," x lt 1),((-5)/(3(x-1)^(2))-2 sin (4x+2)"," x gt 1 ):}`
Given, ` y = (5x)/(3|1-x|) + cos^(2) (2x+1) `
` rArr" " y={{:((5x)/(3(1-x))+cos^(2)(2x+1)", " x lt1),((5x)/(3(x-1))+cos^(2)(2x+1)", " x gt 1):}`
The function is not defined at x = 1.
` rArr (dy)/(dx) ={{:(5/3{((1-x)-x(-1))/((1-x)^(2))}-2 sin (4x+2)", " x lt1),(5/3{((x-1)-x(1))/((x-1)^(2))}-2 sin (4x+2)", " x gt 1):}`
`rArr (dy)/(dx)={{:(5/(3(1-x)^(2))-2 sin (4x+2)", " x lt 1),(-5/(3(x-1)^(2))-2 sin (4x=2)", " x gt 1):}`
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