Differentiation 02

y = 5u^3, u = √(w + 3) and w = x^2 - 4
dy/dx = dy/du * du/dw * dw/dx (by chain rule)
= 15u^2 * 1/2√(w+3) * 1 * 2x
= 15[√(w + 3)]^2 * 1/2√(x^2 - 4 + 3) * 2x
= 15(x^2 - 4 + 3) * x/√(x^2 - 1)
= 15(x^2 - 1) * x/√(x^2 - 1)
= 15x√(x^2 - 1)