If #f(x) =tan^24x # and #g(x) = sqrt(5x1 #, what is #f'(g(x)) #?
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Reqd. Deri.
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To find ( f'(g(x)) ), we first find ( f'(x) ) and then substitute ( g(x) ) into it.
Given ( f(x) = \tan^2(4x) ) and ( g(x) = \sqrt{5x  1} ):

Find ( f'(x) ): ( f'(x) = \frac{d}{dx}[\tan^2(4x)] ) ( f'(x) = 2\tan(4x) \sec^2(4x) \cdot 4 )

Substitute ( g(x) ) into ( f'(x) ): ( f'(g(x)) = 2\tan(4\sqrt{5x1}) \sec^2(4\sqrt{5x1}) \cdot 4 )
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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