How do I find the solution to the following problem using Implicit Differentiation?
#x sin(y) +y sin (x) =2#
2 Answers
Explanation:
#"assuming you require "dy/dx#
#color(blue)"differentiate implicitly with respect to x"#
#"differentiate "xsiny" and "ysinx" using the "color(blue)"product rule"#
#rArrdy/dx(xcosy+sinx)=-siny-ycosx#
#rArrdy/dx=-(siny+ycosx)/(xcosy+sinx)#
Given:
Differentiate each term with respect to x:
Use the product rule on the first term:
where
Substituting into the product rule:
Substituting this into the equation:
Use the product rule on the next term:
where
Substituting into the product rule:
Substituting this into the equation:
The derivative of a constant is 0:
Move all of the terms that do not contain
Factor out
Divide both sides by the leading coefficient: