Property 14
Derivative of Closed Function
\(F(x,y)=0\qquad(y=f(x))\)
\(\boxed{\samefrac{dy}{dx}=-\samefrac{F_x}{F_y}}\)
\(F_x\): Derivative with respect to x. When taking derivative with respect to x, y is thought to be constant.
\(F_y\): Derivative with respect to y. When taking derivative with respect to y, x is thought to be constant.
1.
\(6x^2-12y^2-3x+9=0\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{(1,1)}=?\)
2.
\(5x+y^2+4=0\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{(-1,1)}=?\)
3.
\(4xy-x^2-4=0\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{(2,1)}=?\)
4.
\(2x^3y+3x^2y^3=28\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{(1,2)}=?\)
5.
\(2x^3-8y^3=24\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{x=2}=?\)
6.
\(4x-12y^3=24\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{x=3}=?\)
7.
\(6x^2-12y^2-3x-6=0\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{(2,1)}=?\)