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if y=sinx ,then show that d^2(cos^7x)/dy^2 is equal to 35cos^3x – 42cos^5x

if y=sinx ,then show that d^2(cos^7x)/dy^2 is equal to 35cos^3x – 42cos^5x

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
y=sinx
so dy/dx =cosx
let z=cos7x
dz/dy=7cos6x.(-sinx).dx/dy
=-7cos6xsinx.(1/cosx)
=-7cos5xsinx
d2z/dy2=d/dy(dz/dy)
=d/dx(dz/dy).dx/dy
=d/dx(-7cos5xsinx).(1/cosx)
=-7{cos5x.cosx+sinx.(-5cos4xsinx)}.(1/cosx)
=-7cos5x+35cos3xsin2x
=35cos3x(1-cos2x)-7cos5x
=35cos3x-35cos5x-7cos5x
=35cos3x-42cos5x

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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