# How do you find the instantaneous rate of change of #w# with respect to #z# for #w=1/z+z/2#?

Justification

first configuration.

A sum's derivative is equal to the total of its derivatives.

Identity multiplicative postulate.

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To find the instantaneous rate of change of ( w ) with respect to ( z ) for ( w = \frac{1}{z} + \frac{z}{2} ), you would differentiate ( w ) with respect to ( z ) using the rules of differentiation. This yields ( \frac{dw}{dz} = -\frac{1}{z^2} + \frac{1}{2} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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