Implicit Diffentiation

Question

Use implicit differentiation to find the slope of the tangent line to the curve

 

y/(x-4y)= x^2 +8

 

 

at point (1,  9/37)

 

Answer 1

y/(x-4y)= x^2 +8

 

y=(x^2+8)*(x-4y)=x^3+8x-4yx^2-32y

differential

 

dy/dx=3x^2+8-4(dy/dx)*x^2-8y*x-32(dy/dx)

Move dy/dx's to the same side

 

dy/dx+4(dy/dx)*x^2+32(dy/dx)=3x^2-8y*x

Factor

 

dy/dx(1+4x^2+32)=3x^2-8y*x

 

Divide

 

dy/dx=(3x^2-8y*x)/(1+4x^2+32)

Plug in (1,9/37)