if e^(13x+2y)=13y^2+x

then dy/dx =

Expert Answers

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You need to find `dy/dx`  using implicit differentiation such that:

`e^(13x+2y)*(13 + 2dy/dx) = 13*2y*dy/dx + 1`

Opening the brackets yields:

`13e^(13x+2y) + 2e^(13x+2y)*dy/dx = 26y*dy/dx+ 1`

Moving the terms that contain `dy/dx`  to the left side yields:

`2e^(13x+2y)*dy/dx - 26y*dy/dx = 1 - 13e^(13x+2y)`

Factoring out `2dy/dx`  yields:

`2dy/dx*(e^(13x+2y) - 13) = 1 - 13e^(13x+2y)`

`dy/dx = (1 - 13e^(13x+2y))/(2*(e^(13x+2y)))`

Hence, evaluating `dy/dx` , under the given conditions, yields `dy/dx = (1 - 13e^(13x+2y))/(2*(e^(13x+2y))).`

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