Question

Implicit differentiation

Answer 1

\[\LARGE e^{x/y}=5x-y\]

Answer 2

diff. w.r.t x
\[e ^{\frac{ x }{ y }}\frac{ y*1-x \frac{ dy }{dx } }{ y^2 }=5*1-\frac{ dy }{dx }\]
\[y*e ^{\frac{ x }{ y }}-xe ^{\frac{ x }{y }}\frac{ dy }{dx }=5y^2-y^2\frac{ dy }{dx }\]
\[\left( y^2-xe ^{\frac{ x }{ y }} \right)\frac{ dy }{ dx }=5y^2-ye ^{\frac{ x }{ y }},\]
\[\frac{ dy }{ dx }=\frac{ 5y^2-ye ^{\frac{ x }{y }} }{ y^2-xe ^{\frac{ x }{y }} }\]

Answer 3

for implicit differentiation of y(x), let every mention of y in the problem represent ANY function y(x) whose derivative is y'(x) and can be written simply y'.

on the left side: \[\frac{ d }{ dx } e^{x/y} = e^{x/y}*\frac{ d }{ dx }(x/y) = \]

i'll stop and check answer above ^_^

Answer 4

looks good. every derivative of y is represented as dy/dx

Answer 5

Thanks guys :)