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

1x^2+4xy+4y^3=41 at the point (1,2)

Question

Use implicit differentiation to find the slope of the tangent line to the curve 

1x^2+4xy+4y^3=41  at the point (1,2)

danjs · Answer

hi

anonymous · Answer

hello! I am not sure how to do this problem

danjs · Answer

ok one sec

danjs · Answer

the first term is simply a power rule wrt x

danjs · Answer

the second term, is using the product rule and the chain rule

$$4x \frac{ d }{ dy }(y)\frac{ dy }{ dx }  +  \frac{ d }{ dy }(4y ^{2})\frac{ dy }{ dx }$$

danjs · Answer

the third term is a chain rule:

$$\frac{ d }{ dy }(3y ^{2})\frac{ dy }{ dx }$$

danjs · Answer

You get all that part?

anonymous · Answer

yes I get it so far

danjs · Answer

now you have to solve that equation for dy/dx

danjs · Answer

let dy/dx = y'

danjs · Answer

2x + 4x*y' + 12y^2 *y' = 0

danjs · Answer

solve that for y'

danjs · Answer

then use the point they gave you to find the slope dy/dx at that point

anonymous · Answer

ok thank you i am going to try it