I went through an example question that showed me how to solve the question but I'm not sure if I've misunderstood something or if they did a mistake.(adsbygoogle = window.adsbygoogle || []).push({});

Question: Derivate y = (1/a^{x})^{ax}

ln(y) = ln( (1/a^{x})^{ax}) = ax( ln(1) - ln(a^{x}) ) = -ax ln(a^{x})

(1/y)(dy/dx) = -ax *a- a * ln(a^{x}ln(a)^{x})

dy/dx = (1/a^{x})^{ax}* (-ax * a^{x}ln(a) - a * ln(a^{x}))

I think that they are derivating -ax ln(a^{x}) as a product of two functions with u*(dv/dx) + v*(du/dx) where u = -ax and v = ln(a^{x}). But isn't (dv/dx) supposed to be onlyln(a)? So dy/dx = (1/a^{x})^{ax}* (-ax *ln(a)- a * ln(a^{x}))

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# B Derivation with logarithms and product

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