Derivative of log_x (for any positive base aà ­1) | AP Calculus AB | Khan Academy

[@morgard211]

I did it by myself, but by the implicit method: y = loga(x), which is the same as: a^(y) = x now take the derivative of both sides by also using a formula for a^x: ln(a)a^(y)*(dy/dx) = 1 now just get dy/dx to the left hand side: dy/dx = 1 / (ln(a)a^y) and replace "y" for "loga(x)": dy/dx = 1 / (ln(a)a^(loga(x))) and "a" raised to loga(x) is just "x", so we get: dy/dx = 1 / (ln(a)x).

[@flashsharma4309]

Are khan sir bihari chod diye ka 😂😂

[@SlipperyTeeth]

Related challenge: Find the derivative of log_x(e).

[@ripple123]

d(log_x(e))/dx = 0 ?

[@egor.okhterov]

+Hrsikesa Ramjith why?

[@SlipperyTeeth]

+Hrsikesa Ramjith It's not a constant. I'll give the correct answer tomorrow. By the way, this video explains a great strategy that can be used to solve my problem. Just to clarify, it's the derivative of log base x of e.

[@egor.okhterov]

The first step is log_x(e) = log_e(e) / log_e(x) =)

[@ripple123]

d(log_x(e))/dx = -1/(xln^2(x) ?

[@АлексейЛисиенко-ы9х]

Аляо