# If #f(x) =-e^(2x+4) # and #g(x) = tan3x #, what is #f'(g(x)) #?

Therefore:

Final Answer

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To find ( f'(g(x)) ), first, we need to find ( f'(x) ), then substitute ( g(x) ) into ( f'(x) ):

Given ( f(x) = -e^{2x+4} ) and ( g(x) = \tan(3x) ),

( f'(x) = \frac{d}{dx}(-e^{2x+4}) = -2e^{2x+4} ),

Now, we substitute ( g(x) = \tan(3x) ) into ( f'(x) ):

( f'(g(x)) = -2e^{2g(x)+4} = -2e^{2\tan(3x)+4} ).

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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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