Differentiate (4x 2)^–3 with respect to x. Hence, find the value of dy/dx when x=1?
y = (4x^ 2)^–3
dy/dx = -3 (4x^2)^-4 * d/dx (4 x^2)
= -3 (4x^2)^-4 * 8 x
= 24 x /(4 x^2)^4
= 24 x / (256 x^8)
= 3 / (32 x^7)
3/32
or,
y = 1/64 x^-6
dy/dx = -6/64 x^-7
at x=1, that is
-6/64 = -3/32