If `x=f(t) and y=phi(t),` prove that `(d^2y)/(dx^2)=(f_1phi_2-f_2phi_1)/(f_1^3)` where suffixes denote differentiation `w.r.t.t.`

If x=f(t) and y=phi(t), prove that (d^(2)y)/(dx^(2))=(f_(1)phi_(2)-f_(2)phi_(1))/(f_(1)^(3)) where suffixes denote differentiation w.r.t.

If x=phi(t),y=Psi(t)," then "(d^(2)y)/(dx^(2)) is equal to

If x=f(t) and yy=g(t) are differentiable functions of t then (d^(2)y)/(dx^(2)) is

If x=t+(1)/(t),y=t-(1)/(t)," where "tne0," then: "(d^(2)y)/(dx^(2))=

Given F(x)=f(x)phi(x) and f'(x)phi'(x)=c then prove that F''(x)/F(x)=(f'')/f+(phi'')/phi+2c

If f(x)=(x+1)/x and phi(x)=(x^4+1)/(x^4) then phi(a)=__-- where f(a)=5.

Let y=f(x). phi(x) and z=f'(x). phi'(x) prove that (1)/(y)*(d^(2)y)/(dx^(2))=(1)/(f)*(d^(2)f)/(dx^(2))+(1)/(phi)*(d^(2)phi)/(dx^(2))+(2z)/(f phi)

Y=5sin(3 omega t+phi) where omega and phi are constant.Finf (dy)/(dx)

The second derivative of a single valued function parametrically represented by x=phi(t) and y=psi(t) (where phi(t) and psi(t) are different function and phi'(t)ne0) is given by