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 an

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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. =

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Adalynn 4 weeks 2021-09-19T20:13:08+00:00 1 Answer 0

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    2021-09-19T20:14:14+00:00

    Answer:

    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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