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Why is this wrong? C3 Differentiation.

Differentiating ln(1/3x)


Compare the two workings, the 1st one is correct, the 2nd one is wrong. but Why?

Spoiler

Reply 1
Avatar for Ayman!
Ayman!
15
Original post by SaadKaleem
Differentiating ln(1/3x)


Compare the two workings, the 1st one is correct, the 2nd one is wrong. but Why?

Spoiler



ddx(13x)=13ddx(1x)=−13x2\displaystyle \frac{\mathrm{d} }{\mathrm{d} x}\left ( \frac{1}{3x} \right )= \frac{1}{3}\frac{\mathrm{d} }{\mathrm{d} x}\left ( \frac{1}{x} \right )= -\frac{1}{3x^{2}}
(edited 8 years ago)
Reply 2
Avatar for SaadKaleem
SaadKaleem
OP
8
Original post by aymanzayedmannan
ddx(13x)=13ddx(1x)=−13x2\displaystyle \frac{\mathrm{d} }{\mathrm{d} x}\left ( \frac{1}{3x} \right )= \frac{1}{3}\frac{\mathrm{d} }{\mathrm{d} x}\left ( \frac{1}{x} \right )= -\frac{1}{3x^{2}}


Alright, thank you... can be quite tempting to write it as (3x)^-1
Reply 3
Avatar for Ayman!
Ayman!
15
Original post by SaadKaleem
Alright, thank you... can be quite tempting to write it as (3x)^-1


axnax^{n} can be written as (anx)n\left( \sqrt[n]{a}x \right )^{n} but d(axn)dx≠(anx)n−1\frac{\mathrm{d}\left ( ax^{n} \right ) }{\mathrm{d} x} \neq \left ( \sqrt[n]{a}x \right )^{n-1}.

Remember than constants are unchanged when differentiating (or integrating) linear functions.
Reply 4
Avatar for SaadKaleem
SaadKaleem
OP
8
Original post by aymanzayedmannan
axnax^{n} can be written as (anx)n\left( \sqrt[n]{a}x \right )^{n} but d(axn)dx≠(anx)n−1\frac{\mathrm{d}\left ( ax^{n} \right ) }{\mathrm{d} x} \neq \left ( \sqrt[n]{a}x \right )^{n-1}.

Remember than constants are unchanged when differentiating (or integrating) linear functions.


Thanks once again. :smile:

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