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collge calculus

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find the derivative of y=[(4^(7x))(7^(4x))]/[10^(e)]

without using logarithmic differentiation!

  • collge calculus -

    1/10^e is a constant that you can leave in that form, as a multiplier of the derivative.

    Use the product rule for the rest.

    For the derivative of 4^7x, let 7x = u
    d/dx 4^(7x) = d/du 4^u * d(7x)/dx
    = 4^u * ln4 * 7
    = 7 ln4 * 4^(7x)

    d/dx 7^(4x) = 4 ln7* 7^(4x)

    Put it all together

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