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March 25, 2017

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Compute the derivative of f(x)=5^x^2+1 using logarithmic differentiation.

  • Calc - ,

    Check using the following formula:

    (5^g(x))'= (ln5)*(5^g(x))*(g'(x))

  • Calc - ,

    I never did like formulas.

    remember that derivative of ln(g(x))=g'(x)/g(x)
    here f(x)=5^(x^2+1)
    ln f(x)= (x^2+1)ln5
    take the derivative
    f'(x)/f(x)=2x*ln5 + 0
    f'(x)=f(x)*10x*ln5=10x*ln5*5^(x^2+1)

    Now comparing this to your 'formula':
    f'(x)=ln5*5^(x^2+1)*2x=10x*5^(x^2+1)

    Hmmm same thing.

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