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Math Help - [SOLVED] Extending Differentiation: Chain Rule

  1. #1
    Member looi76's Avatar
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    [SOLVED] Extending Differentiation: Chain Rule

    Question:
    Use the substitution u = 5x + 3 to differentiate the following with respect to x.

    (a)  y = (5x + 3)^6

    (b)  y = (5x + 3)^{\frac{1}{2}}

    (c)  y = \frac{1}{5x + 3}

    Can you please show be the steps for solving (a) using the chain rule?
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  2. #2
    Moo
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    Hello,

    Substituting :

    y=u^6

    The chain rule says :

    y=f(u(x)) \Longleftrightarrow \frac{dy}{dx}=\frac{du}{dx} f'(u(x))

    Here, f(u)=u^6



    \frac{dy}{dx}=6 \frac{du}{dx} u^5

    \frac{du}{dx}=5

    Hence \frac{dy}{dx}=30u^5=30 (5x+3)^5

    Is it clear enough ?
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