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Math Help - derivative question

  1. #1
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    derivative question

    derivative of 10^7x squared.
    the log part kinda throws me. any help
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  2. #2
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    Is this the question: \frac{d}{dx} \left(10^{7x}\right)^2 ?

    If so, first simplify:
    = \frac{d}{dx} {\color{red}10^{{\color{blue}14x}}} \qquad \text{Since: } \left(a^{b}\right)^c = a^{bc}

    Then, use the chain rule:
    = \underbrace{{\color{red}10^{{\color{blue}14x}}} \ln 10}_{\displaystyle (a^x)' = a^x \ln a} \cdot \left({\color{blue}14x}\right)'

    = \hdots
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  3. #3
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    I wish, it would be simplier.

    The x is squared. no parentheses.
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  4. #4
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    \frac{d}{dx} {\color{red}10}^{{\color{blue}7x^2}}

    Not any different, just apply the chain rule:

    = \underbrace{{\color{red}10}^{{\color{blue}7x^2}}\l  n 10}_{\displaystyle (a^x)' = a^x \ln a} \cdot \ \ \left({\color{blue}7x^2}\right)'
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