derivative of ln(1/x) vs derivative of 1/ln(x)

Показать описание

Many calculus students tend to make misteaks when taking the derivative of ln(1/x) vs the derivative of 1/ln(x). For the derivative of ln(1/x), we can actually use a log property to simplify the expression first before taking the derivative so we don't need to use the quotient rule. For the derivative of 1/ln(x), we can write it as (ln(x))^-1 and then use the power rule and the chain rule to find the derivative. Subscribe to @bprpcalculusbasicsfor more calculus tutorials!

-------------------
If you find this channel helpful and want to support it, then you can
join the channel membership and have your name in the video descriptions:
buy a math shirt or a hoodie (10% off with the code "WELCOME10"):
-------------------
😊 Thanks to all channel members 😊
Sandglass Dªrksun Seth Morris Andrea Mele

---------------------------------------------------------
---------------------------------------------------------
Best wishes to you,
#justcalculus

Рекомендации по теме

Комментарии

0:28 Yes, I remember the *loy* property

Jaojao_puzzlesolver

Cool video, learning some calculus right now and I get tripped up with logarithms sometimes. Thanks a lot!

browhat

Also fun to just use the chain rule on the first one, to check.

Outside derivative: let v = 1/x; d/dv(ln v) = 1/v = 1/(1/x) = x
Inside derivative: d/dx(1/x) = d/dx(x^(-1)) = (-x^(-2)) = -1/(x^2)
Multiply together: x * -1/(x^2) = -x/(x^2) = -1/x

(It was not easy trying to figure out how to write all the steps.)

ZipplyZane

for y = 1 / ( ln x )
I like to use the chain rule.

Let u = ln x

so y = 1 / u
dy / dx = - 1 / u^2
du / dx = 1 / x

so dy / dx = [- 1 / ( ln x )^2 ] * ( 1 / x )

michaelempeigne

Technically doing the chain rule + derivative power rule for ln(1/x) does still work fine albiet over complicating it

SJrad

My first thought was to use the logarithm rule to simplify ln(a/b) = ln a - ln b, which gives ln(1/x) = ln 1 - ln x = -ln x, then differentiate to obtain -1/x

ElementaryLord

Can you do more series questions instead of just derivatives and integrals and limits. Show Calc BC kids some love

joser

I have a request. Can you prove the law of cosines without pethagon
theorem for me? Ever since I learned law of cosines I thought it can be a method to prove pethagon theorem but I just saw a proof of cosines that involves pethagon theorem so using it would be circular reasoning

wristdisabledwriter

❤ how can i solve for the derivative of ln(1+x)^4

albertomaths

Hey bprp, what do you think of ln^2(x) notation for power of ln

emmecuh

derivative of ln(1/x) vs derivative of 1/ln(x)

derivative of ln(1/x) vs derivative of 1/ln(x)

Derivative of ln(1/x), calculus 1 tutorial

how do we know the derivative of ln(x) is 1/x (the definition & implicit differentiation)

Proof: the derivative of ln(x) is 1/x | Advanced derivatives | AP Calculus AB | Khan Academy

Derivative of ln(1/x) / Chain Rule vs. Power Rule

How to find the derivative of 1/x and ln(x). #calculus #ai #derivatives

Take the derivative of the natural log function

derivative of ln(1+1/x), two ways

Derivative of Logarithmic Functions

Why is the derivative of lnx = 1/x?

Calculus: First and Second Derivative of ln x /(1 + ln x)

Derivative of ln(1/x) #shorts #calculus

Derivative of ln(x+1) #shorts #calculus

Find The Derivative Of ln(ln(1-x)). The Derivative Of Logarithms

Introduction to Logarithmic Differentiation

The PROOF that the Derivative of ln(x) equals 1/x!!! | Limit Definition of Derivatives

Find the derivative of ln(1/x)+1/lnx

Proof: Derivative of ln(x) = 1/x by First Principles

Derivative of ln(x)/x #shorts #calculus

Derivative of f(x) = ln(1/x^2)

The Derivative of ln x

Derivative of ln (x) using the definition of derivative

Derivative of ln(sin(x)), chain rule with natural log and sine. #shorts

😳 CLEAN BASIC CALCULUS Differentiate d/dx(ln1/x)=? #Shorts