# Implicit Differentiation

Homework Statement:
Find the implicit differentiation
Relevant Equations:
(sinx)^(cosy)+(cosx)^(siny)=a
The working I've tried is in the attachment.

#### Attachments

• 15980283088327760621644651835670.jpg
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fresh_42
Mentor
I guess people do not want to download your picture, then rotate it, zoom in, only to find out that they cannot read it anyway.

Here is how to type formulas on PF (it's not difficult):
https://www.physicsforums.com/help/latexhelp/

Blurry__face14
benorin
Homework Helper
Gold Member
I'm not gonna follow your work, too taxing: I get this solution

$$\tfrac{dy}{dx}=\tfrac{( \cos x)^{\sin y}\sin y \tan x - ( \sin x)^{\cos y}\cos y \cot x}{( \cos x )^{ \sin y } \cos y \log \cos x - ( \sin x) ^{\cos y} \sin y \log \sin x}$$

Blurry__face14 and etotheipi
I guess people do not want to download your picture, then rotate it, zoom in, only to find out that they cannot read it anyway.

Here is how to type formulas on PF (it's not difficult):
https://www.physicsforums.com/help/latexhelp/
Ahh, I apologise.
I've tried using Latex as you have asked, but I'm afraid it's taking way too long to type out my working.
However, I've taken a better photo, I'm not confident in my working but please do check. Thank you :)

#### Attachments

• Implicit Differentiation.pdf
262.5 KB · Views: 49
I'm not gonna follow your work, too taxing: I get this solution

$$\tfrac{dy}{dx}=\tfrac{( \cos x)^{\sin y}\sin y \tan x - ( \sin x)^{\cos y}\cos y \cot x}{( \cos x )^{ \sin y } \cos y \log \cos x - ( \sin x) ^{\cos y} \sin y \log \sin x}$$
Thank you for the answer. But may I ask what working you've done to solve this?

benorin
Homework Helper
Gold Member
You forgot the chain rule when differentiating functions of y you need to multiply by y' from the chain rule, that'll give an equation involving y', solve it.

Blurry__face14