Recall the following formula:

     if   y = xⁿ ,  then   y' = nx^n-1 

You are given the following:

     y = 5x^-4 + 3x^-1 

We can compute the derivative of y using the formula above:

     y' = (-4)5x^-4-1 + (-1)3x^-1-1 

        = -20x^-5 - 3x^-2

The answer is usually accepted in this form. Recall that negative exponents can be changed to positive exponents by taking their reciprocal. That is, 

     y' = -20x^-5 - 3x^-2 

        = -20(x^-5/1) - 3(x^-2/1)

        = -20(1/x⁵) - 3(1/x²)

        = -20/x⁵ - 3/x² 

Remember that the power rule for derivatives states that you need to multiple the coefficient by the power and subtract one from the power.

y = 5x^-4 + 3x^-1               Given

y' = (-4)5x^-5 + (-1)3x^-2   Power Rule

y '= -20x^-5 - 3x^-2            Simplify

This answer can also be written as y' = -20/x⁵ - 3/x².