if x=4(z)^2 + 5 , y=6(z)^2 + 7z + 3 find d2y/dx2

x=4z^2+5, y= 6z^2+7z+3

Diff. w. r. to z , we get

dx/dz=8z and dy/dz= 12z+7

dy/dx=(dy/dz)/(dx/dz)=(12z+7)/8z= 3/2 + 7/(8z)

d²y/dx²=d/dx(dy/dx)

=d/dz(dy/dx).dz/dx

=d/dz)(3/2 +7/(8z)).dz/dx

=-7/8z². 1/8z=-7/64z³

Thanks & Regards

Rinkoo Gupta

askIITians Faculty

dy/dx = (dy/dz)/(dx/dz) = (12z + 7)/8z
d2y/dx2 = d(dy/dx)/dt / (dx/dt) = (12z^2 - 12z - 7 )/ 64.z^3
Thanks

x=4z^2+5; dx/dz=8zy=6z^2+7z+3; dy/dz=12z+7dy/dx=12z+7/8zDifferentiating again w.r.t xd^2y/dx^2=-7/64z^3