Question

Find dy/dx for y=ln(5−x)^6

Answer 1

\[y = \ln(5-x)^6\]

take derivative :

\[\frac{dy}{dx} = 6 \cdot \ln(5-x)^5 \frac{d(5-x)}{dx}\]

Answer 2

It is by chain rule..
In chain rule we are using power rule also which says :

\[y = f(x)^n\]

\[\frac{dy}{dx} = n \cdot f(x)^{n-1} \cdot \frac{d(f(x))}{dx}\]

Answer 3

Wait, isn't that in the case that the 6th power would be to the entire thing? I thought you brought the 6 in front since lna^b=blna

Answer 4

\[\frac{dy}{dx} = 6 \cdot \ln(5-x)^5 \frac{d(\ln(5-x)}{dx} \cdot \frac{d(5-x)}{dx}\]

Answer 5

ln((x-5)^6) = 6ln(x-5)

( 6ln(x-5) ) ' = 6/(x-5)

Answer 6

Mixing up things...

Answer 7

oh! duh! Got it, thank you!!1

Answer 8

\[y = \ln(5-x)^6\]

\[\frac{dy}{dx} = \frac{1}{(5-x)^6} \times 6 \times (5-x)^5 \times (-1)\]

Answer 9

Is this right???

Answer 10

It will reduce to :

\[\frac{dy}{dx} = \frac{-1}{(5-x)}\]

Answer 11

ln((5-x)^6) = 6ln(5-x)

( 6ln(5-x) ) ' = -6/(5-x)

Answer 12

Forgot 6 there..

Oh God...

Answer 13

\[\frac{dy}{dx} = \frac{-6}{(5-x)}\]

Answer 14

Yes by power rule, you can bring 6 in front:

\[y = 6 \cdot \ln(5-x)\]

Now take the derivative..

Answer 15

Okay, I've got it figured out! Thank you! If you'd like to help some more I just posted another question :)