How do you differentiate #y=(6x^2 + 2x)^3#?
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To differentiate the function y=(6x^2 + 2x)^3, you can use the chain rule. The chain rule states that if you have a composite function, f(g(x)), then the derivative is f'(g(x)) times g'(x). Applying this to the given function:

Find the derivative of the outer function: Let u = 6x^2 + 2x Then y = u^3 dy/du = 3u^2

Find the derivative of the inner function: du/dx = d(6x^2 + 2x)/dx = 12x + 2

Multiply the derivatives found in steps 1 and 2: dy/dx = (dy/du) * (du/dx) = 3(6x^2 + 2x)^2 * (12x + 2)
So, the derivative of y=(6x^2 + 2x)^3 is dy/dx = 3(6x^2 + 2x)^2 * (12x + 2).
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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.
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