if e^(13x+2y)=13y^2+x then dy/dx =
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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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