Question

find dy/dx implicitly of 6e^(xy)-2x=y^2+13x^2

Answer 1

What part are you having trouble with? The exponential? :O

Answer 2

\[\huge (6e^{xy})' \quad = \quad 6e^{xy}(xy)'\]The exponential will give us the same thing back, but we also must apply the chain rule - Multiplying by the derivative of what was in the exponent.

Answer 3

Product rule :O
\[\huge 6e^{xy}(xy)'\quad =\quad 6e^{xy}\left((x)'y+x(y)'\right)\]

Answer 4

\[\huge = \quad 6e^{xy}\left(y+x\cdot y'\right)\]