Question

x = Sint
y = cost
find d^y/dx^2
​

Answer 1

Answer :(d²y /dx²) = -sec³t.

Step-by-step explanation:

As we have given the two functions

x = sint, y = cost ,here the parameter is t, so differentiate both the functions with respect to t

x = sint , Differentiation wrt t

(dx/dt) = d/dt(sint)

= cost

Now, y = cost , Differentiate wrt

(dy/dt)= d/dt(cost)

= -sint

we know,dy/dx = (dy/dt)/(dx/dt)

= (-sint) /(cost)

= - tant

Again , Differentiate wrt x

(d²y /dx²) = -sec²t x (dt /dx)

= -sec²t x [1/(dx/dt)]

= -sec²t x [1/(cost) ]

= -sec²t x sect = -sec³t

(d²y /dx²) = -sec³t.