Nicolee H.

asked • 09/27/17# implicit differentiation (Mathematics)

Find dy/dx for e^(2x+3y) = x^2 -ln (xy^3)

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## 1 Expert Answer

Victoria V. answered • 09/28/17

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e

^{(2x+3y)}= x^{2}- ln(xy^{3})Nicolee, the first thing I would do would be to expand the "ln" using logarithm properties to keep from doing a complicated chain rule.

e

^{(2x+3y)}= x^{2}- (lnx + 3lny)e

^{(2x+3y)}= x^{2}- lnx -3lnyNo differentiate each side

deriv of e

^{anything}is e^{anything}* deriv of "anything". So the left side becomese

^{(2x+3y)*[2 + 3 (dy/dx)] }diff the right side and get 2x - (1/x) - 3(1/y)(dy/dx)

distribute on the left

e

^{(2x+3y)}(2) + e^{(2x+3y)}[3(dy/dx)] = 2x - (1/x) -(3/y)(dy/dx)Now put all the (dy/dx)'s on the left. Put everything else on the right.

Factor a (dy/dx) out of every term on the left

And divide both sides by the stuff on the left in the parentheses.

Sorry - gotta run or I would show these steps...

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Michael J.

09/27/17