# How do you differentiate #f(x) = 5e^x - 3x^4 + 9x + 16#?

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To differentiate the function ( f(x) = 5e^x - 3x^4 + 9x + 16 ), you can apply the rules of differentiation.

The derivative of ( e^x ) is ( e^x ), and the derivative of ( x^n ) with respect to ( x ) is ( nx^{n-1} ).

So, differentiating each term: [ f'(x) = 5(e^x) - 3(4x^3) + 9 + 0 ]

Simplify this to get the derivative: [ f'(x) = 5e^x - 12x^3 + 9 ]

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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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