How do you differentiate #y=-5^(4x^3)#?
you have to use chain rule to differentiate this function. this is how you do it,
suppose, a=5 so,
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To differentiate ( y = -5^{4x^3} ), you can use the chain rule.
The derivative of ( -5^{4x^3} ) with respect to ( x ) is:
[ \frac{dy}{dx} = \frac{d}{dx}(-5^{4x^3}) = -5^{4x^3} \cdot \ln(5) \cdot \frac{d}{dx}(4x^3) ]
Using the chain rule, the derivative of ( 4x^3 ) with respect to ( x ) is ( 12x^2 ).
So, the final derivative is:
[ \frac{dy}{dx} = -5^{4x^3} \cdot \ln(5) \cdot 12x^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.
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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