How do you determine #(dy)/(dx)# given #f(x)=(3x^4-7)^10#?
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To determine (dy)/(dx) given f(x) = (3x^4 - 7)^10, you would need to differentiate the function f(x) with respect to x using the chain rule.
First, apply the chain rule, which states that if you have a function raised to a power, you need to multiply by the derivative of the inner function:
dy/dx = d/dx [(3x^4 - 7)^10]
Then, apply the chain rule:
dy/dx = 10(3x^4 - 7)^9 * d/dx (3x^4 - 7)
Now, differentiate the inner function, 3x^4 - 7, with respect to x:
d/dx (3x^4 - 7) = 12x^3
Substitute this result back into the equation:
dy/dx = 10(3x^4 - 7)^9 * 12x^3
This simplifies to:
dy/dx = 120x^3(3x^4 - 7)^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.
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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