## anlnt4 3 years ago Find dy/dx for y=ln(5−x)^6

1. waterineyes

$y = \ln(5-x)^6$ take derivative : $\frac{dy}{dx} = 6 \cdot \ln(5-x)^5 \frac{d(5-x)}{dx}$

2. anlnt4

3. waterineyes

It is by chain rule.. In chain rule we are using power rule also which says : $y = f(x)^n$ $\frac{dy}{dx} = n \cdot f(x)^{n-1} \cdot \frac{d(f(x))}{dx}$

4. anlnt4

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

5. waterineyes

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

6. Algebraic!

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

7. waterineyes

Mixing up things...

8. anlnt4

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

9. waterineyes

$y = \ln(5-x)^6$ $\frac{dy}{dx} = \frac{1}{(5-x)^6} \times 6 \times (5-x)^5 \times (-1)$

10. waterineyes

Is this right???

11. waterineyes

It will reduce to : $\frac{dy}{dx} = \frac{-1}{(5-x)}$

12. Algebraic!

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

13. waterineyes

Forgot 6 there.. Oh God...

14. waterineyes

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

15. waterineyes

Yes by power rule, you can bring 6 in front: $y = 6 \cdot \ln(5-x)$ Now take the derivative..

16. anlnt4

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