# How do you find the derivative of #w=(1+4x^3)^-2#?

The solution is given below.

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To find the derivative of ( w = (1 + 4x^3)^{-2} ), you can use the chain rule. First, rewrite the function as ( w = (1 + 4x^3)^{-2} = (1 + 4x^3)^{-1} \cdot (1 + 4x^3)^{-1} ). Then differentiate each part separately. The derivative of ( (1 + 4x^3)^{-1} ) with respect to ( x ) is ( -1 \cdot (1 + 4x^3)^{-2} \cdot 12x^2 ). So, the derivative of ( w ) with respect to ( x ) is ( -2 \cdot (1 + 4x^3)^{-3} \cdot 12x^2 ).

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