If x e 9 y + y 4 sin ⁡ ( 4 x ) =...

vasorasy8

vasorasy8

Answered

2022-06-30

If x e 9 y + y 4 sin ( 4 x ) = e 8 x implicitly defines y as a function of x then what is d y d x ?

Answer & Explanation

Keely Fernandez

Keely Fernandez

Expert

2022-07-01Added 14 answers

Implicitl differentiation means that we need to treat y as a function of x and apply Chain Rule. You also forgot to apply Product Rule to the first term. The derivative of the first term is:
d d x [ x e 9 y ] = x [ d d x e 9 y ] + [ d d x x ] e 9 y = x e 9 y [ d d x 9 y ] + [ 1 ] e 9 y = x e 9 y [ 9 d y d x ] + e 9 y = 9 x e 9 y y + e 9 y
Now do the same thing for the second term, then solve for y′

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