Question

find d^2y/dx^2 of y^2=9x^2+8x

Answer 1

@pclende Should you try the first derivative?

Answer 2

This is asking for the second derivative of y^2=9x^2+8x

1. Take the first derivative:
2y dy/dx = 18x + 8

solve for dy/dx: dy/dx = (18x+8)/2y

2. Take the second derivative since we already know what dy/dx is:

using the quotient rule: d^2y/dx^2 = (18(2y) - 2dy/dx(18x+8))/(2y)^2

Simplify: (36y - (36x+16) dy/dx) / 4y^2

since we already know what dy/dx is, plug it in (it easier to see this with a drawing, one second.