Question

find dy/dx using the chain rule. y=(u^4-4)^3, u=x^-2

Answer 1

so chain rule is take derivative of outer function and keep the inner function then multiply by derivative of inner function so



we can simplify this first so it would be
3( x^(-8) - 4)^2
take derivative of outer which is
3( x^(-8) - 4)^2
multiply by derivative of inner
3( x^(-8) - 4)^2 (-8(x^(-9))
simplify
dy/dx = -24(x^(-8) - 4)(x^(-9))