If y=sin(x/7), then d^2y/dx^2 =?

Question

can someone please help me on this problem?

Answer 1

The function is y = sin(x /7).

Differentiating the above equation.

dy/dx = cos(x /7) * d/dx(x /7)                            ( d/dx(sin x) = cos x )

dy/dx = (1/7)cos(x /7)                                       ( d/dx(x) = 1)

Again differentiating the above equation.

d^y/dx^2 = d/dx[ (1/7)cos(x /7) ]

              = (1/7)d/dx[ cos(x /7) ]

              = (1/7)(- sin(x /7))(1/7)                       ( d/dx(cos x) = - sin x )

              = (- 1/49)sin(x /7).

The second derivative of the function is (- 1/49)sin(x /7).