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Question Number 152918 by ZiYangLee last updated on 03/Sep/21

Find the first derivative of y=x(√(16−x^2 ))+16sin^(−1) (x/4)

Findthefirstderivativeofy=x16−x2+16sin−1x4

Answered by puissant last updated on 03/Sep/21

y=x(√(16−x^2 ))+16arcsin((x/4)) (dy/dx)=(√(16−x^2 ))−((2x^2 )/(2(√(16−x^2 ))))+16((1/4)/( (√(1−(x^2 /(16)))))) =(√(16−x^2 ))−((x^2 (√(16−x^2 )))/(16−x^2 ))+((16(√(16−x^2 )))/(16−x^2 )) =(√(16−x^2 ))+(√(16−x^2 ))(((16−x^2 )/(16−x^2 ))) =2(√(16−x^2 ))..

y=x16−x2+16arcsin(x4)dydx=16−x2−2x2216−x2+16141−x216=16−x2−x216−x216−x2+1616−x216−x2=16−x2+16−x2(16−x216−x2)=216−x2..

Commented by ZiYangLee last updated on 04/Sep/21

thanks sir

thankssir

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