How would I do these problems using Implicit Differentiation? I don't understand how to do them. Help?Find d y / d x if cos ⁡ ( 4 x ) − 2 x e 4 y = 0.andFind slope of the tangent line to the curve 12 x + 8 y + 2 x y = 12 at the point ( 4 , 2 ).

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How would I do these problems using Implicit Differentiation? I don&#039;t understand how to do them. Help?Find   d  y      /    d  x if   cos  ⁡  (  4  x  )  −  2  x      e          4      y        =  0.andFind slope of the tangent line to the curve       12    x    +    8    y    +      2    x    y    =  12 at the point   (  4  ,  2  ).

helsedel1v · Accepted Answer

Differentiate both sides of the equation with respect to   x, remembering that   y is supposed to be a function of   x. So, for example, the derivative of       y    2   would be   2  y                    d        y                    d        x            . Then solve for                     d        y                    d        x            . If you are asked for the slope at a point, substitute the   x and   y values for that point in your expression for                     d        y                    d        x            .

Licinilg · Accepted Answer

I&#039;m guessing this is homework, so I won&#039;t try to provide a complete solution to either of your questions.If you differentiate your first equation with respect to   x, you get  −  4  sin  ⁡  4  x  −  2      e          4      y        −  8  x  y      e          4      y                  d      y              d      x        =  0which you should be able to rearrange.If you differentiate the equation in your second question with respect to   x, you get            12      +      8                        d          y                          d          x                            2              12        x        +        8        y              +            2      y      +      2      x                        d          y                          d          x                            2              2        x        y              =  0and you can then substitute in your   x and   y values.

How would I do these problems using Implicit Differentiation? I don't understand how to do them. Help? Find dy/dx if cos(4x)−2xe4y=0. AND Find slope of the tangent line to the curve 12x+8y−−−−−−−√+sqrt(2xy)=12 at the point (4,2).

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