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# find y' for y=5x^-4+3x^-1

Recall the following formula:

if   y = xn ,  then   y' = nxn-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.

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