Differentiate y = ln(x6 + 4). SOLUTION To use the Chain Rule, we let u = x6 + 4. Then y = ln(u), so dy dx = dy du du dx = Incorrect: Your answer is incorrect. du dx = 1 x6 + 4 Correct: Your answer is correct. =

dy/dx = (6x^5)/(x^6 + 4)

Step-by-step explanation:

We wish to differentiate the given function

y = ln(x^6 + 4).

Consider the Chain rule.

If y = f(u), and u = u(x)

Then

dy/dx = dy/du × du/dx

Now, since we have

y = ln(x^6 + 4)

Let u = x^6 + 4

Then y = ln(u)

dy/du = 1/u

du/dx = 6x^5

dy/dx = dy/du × du/dx

= (1/u) × 6x^5

But u = x^6 + 4

So,

dy/dx = (6x^5)/(x^6 + 4)

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step-by-step explanation: