Answer to Question #7840 in Calculus for Samantha

Question

Implicit Differentiation of the following
1.) (3xy+7)^2=18y
2.) 4y^2=(3x-2)/(3x+2)
3.)x=sin y
4.) x+cot(xy)=1
5.) x^4+sin y=x^3y^5

Answer 1

1.
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2. 4y^2=(3x-2)/(3x+2)here we can easily derive expression for y:
y=+-0.5sqty((3x-2)/(3x+2)) and then derive it as usual

3. x=sin y
here we can also derive expression for y:
y=sin^-1(x)
so y'=1/sqrt(1-x^2)