Extension: Logarithmic Differentiation
Read this topicExplanations 2
- Let's start off with a nice, simple question on derivatives: As you're probably thinking right now, this function is way too complicated to differentiate directly. (Of course yo…
By Steven Kwon, Po-Shen Loh, Alex Federspiel
- (Videos) Logarithmic Differentiation by PatrickJMT Here's a video by patrickJMT showing how to solve problems using logarithmic differentiation. Logarithmic differentiation is d…
By Alex Federspiel
Problems 10
- What is the derivative of xx2x^{x^2}xx2?
- Let ω\omegaω be a primitive 200720072007th root of unity, i.e. a complex number such that ω2007=1\omega^{2007} = 1ω2007=1 but ωk≠1\omega^k \ne 1ωk=1 for k=1,2,…,2006k=1,2,\dots…
- What is the derivative of y=xexy= x^{e^x}y=xex?
- What is the derivative of y=(cosx)x2y = (\cos x)^{x^2}y=(cosx)x2?
- Compute the derivative of f(x)=(xx)(xx)f(x) = \left( x^x \right)^{\left( x^x \right)}f(x)=(xx)(xx) at x=1x = 1x=1. \\ Reminder. ddx(xx)=xx⋅(1+lnx)\frac {\mathrm{d}}{\mathrm{d}x…
- What is the derivative of log(xx2)\log (x^{x^2})log(xx2)?
- Let y=xxy = x^xy=xx for x>0x > 0x>0. What is dydx\frac{dy}{dx}dxdy?
- Find the derivative of y=xxy=x^xy=xx
- Differentiate xy=yxx^y=y^xxy=yx
- Find the derivative of y=(sinx)lnxy=(\sin x)^{\ln x}y=(sinx)lnx