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)

Answer 1

hi

Answer 2

hello! I am not sure how to do this problem

Answer 3

ok one sec

Answer 4

the first term is simply a power rule wrt x

Answer 5

the second term, is using the product rule and the chain rule

\[4x \frac{ d }{ dy }(y)\frac{ dy }{ dx } + \frac{ d }{ dy }(4y ^{2})\frac{ dy }{ dx }\]

Answer 6

the third term is a chain rule:

\[\frac{ d }{ dy }(3y ^{2})\frac{ dy }{ dx }\]

Answer 7

You get all that part?

Answer 8

yes I get it so far

Answer 9

now you have to solve that equation for dy/dx

Answer 10

let dy/dx = y'

Answer 11

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

Answer 12

solve that for y'

Answer 13

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

Answer 14

ok thank you i am going to try it