# How do you differentiate #g(z) = z^2cos(z)e^(2+z)# using the product rule?

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To differentiate ( g(z) = z^2 \cos(z) e^{2+z} ) using the product rule:

- Identify the two functions: ( f(z) = z^2 \cos(z) ) and ( h(z) = e^{2+z} ).
- Apply the product rule: ( g'(z) = f(z)h'(z) + f'(z)h(z) ).
- Find the derivatives of ( f(z) ) and ( h(z) ): ( f'(z) = 2z\cos(z) - z^2\sin(z) ) (using the product rule and the derivative of ( \cos(z) )) ( h'(z) = e^{2+z} ) (using the derivative of ( e^{2+z} )).
- Substitute the derivatives and original functions into the product rule formula: ( g'(z) = (z^2 \cos(z)) \cdot e^{2+z} + (2z\cos(z) - z^2\sin(z)) \cdot e^{2+z} ).
- Simplify the expression if needed.

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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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