
PreCalculus PreCalculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 6th, 2017, 04:15 AM  #1 
Senior Member Joined: Jan 2016 From: Blackpool Posts: 104 Thanks: 2  Difference between partial and implicit differentiation
Hi guys the question is: Find the equations of the tangent and normal lines to the curve 3x^214xy+8y^225=0 at the point P = (−1, 1). would i use partial or implicit differentiation here? Thanks ! 
June 6th, 2017, 04:46 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 
Use implicit differentiation to determine $\dfrac{dy}{dx}$, then evaluate at (1,1) to find the tangent slope ... opposite reciprocal of that value to get the normal slope. Equations of both lines may be found using the pointslope form. 
June 6th, 2017, 09:50 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
"Partial differentiation" is used when you have a function, say, f, of two independent variables, x and y. "Implicit differentiation" is used when you have a formula in two variable, such as x and y, and one variable, y, is a function of the other. Here, you are not given a function of x and y but, rather, an expression involving x and y, and you are thinking of y as a function of x. so, differentiating with respect to x, . Then so . You can use "partial differentiation" to get that result by thinking of "f" as a function of x and y . If, also, you think of x and y as functions of some third variable, u, using the chain rule, . Since f(x, y) was a constant, its derivative with respect to any variable is 0: . Now, take u= x so that dx/du= dx/dx= 1 and dy/du= dy/dx. That previous equation becomes . From that as before. 

Tags 
difference, differentiation, implicit, partial 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Difference between vector differentiation and parametric differentiation  Mr Davis 97  Calculus  1  March 9th, 2015 04:50 AM 
Implicit differentiation  The_Ys_Guy  Calculus  7  January 5th, 2015 07:29 AM 
Implicit Differentiation  khhyle  Calculus  1  February 25th, 2013 04:40 PM 
Implicit Differentiation  mathkid  Calculus  2  September 25th, 2012 11:27 AM 
Implicit Differentiation HELP!!!!!!!!  ohspyro89  Calculus  4  October 6th, 2008 05:48 AM 