Question

Differentiate the function. $r(z)=z^{-5}-z^{1 / 2}$ 

   Differentiate the function.
 $r(z)=z^{-5}-z^{1 / 2}$
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 3, Problem 10 ↓
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Differentiate the function. $r(z)=z^{-5}-z^{1 / 2}$
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00:01 So we're given r of z, so z is your independent variable, is equal to z to the negative fifth, minus z to the one -half.
00:13 And the theme in this problem, as long as your exponent is a rational number, so let me just use different function notation, some constant times x to the n power.
00:27 Maybe i should even mention that n needs to be a rational number.
00:32 Well, i guess it doesn't have to be rational.
00:35 Could even be a real number.
00:36 So let me just ignore that i said that.
00:39 That the derivative is equal to multiplying the coefficient in front times the exponent and then you subtract one from the exponent...
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