Find dy/dx by implicit differentiation. 3 x 2 + 3 = ln ⁡ 5 x y 2 This is what i did: 6 x = D ( ln ⁡ 5 x + ln ⁡ 5 y 2 ) But i was thinking i could also use this way: 6 x = D ( 5 x y 2 ) / 5 x y 2 Are both ways the same?

Question

Find dy/dx by implicit differentiation.   3      x    2    +  3  =  ln  ⁡  5  x      y    2  This is what i did:   6  x  =  D  (  ln  ⁡  5  x  +  ln  ⁡  5      y    2    ) But i was thinking i could also use this way:  6  x  =  D  (  5  x      y    2    )      /    5  x      y    2  Are both ways the same?

Jaydan Gilbert · Accepted Answer

Yes, you are right.If you try the first one, we get,            d                      d            x        (  ln  ⁡  5  x  +  ln  ⁡      y    2    )  =      1          5      x        (            d                      d            x        (  5  x  )  )  =      1    x  In case of the second, we get,                              d                                      d                    x                    (      5      x              y        2            )              5      x              y        2              =            5              y        2                    5      x              y        2              =      1    x  yielding the same answer as before.Hope it helps.

Find dy/dx by implicit differentiation. 3x^2+3 = ln 5xy^2

Open question

Answer & Explanation

New Questions in Calculus 2