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Partial derivatives if ` (x,y) =ln (9xy^4 +14)`

Partial derivatives if ` (x,y) =ln (9xy^4 +14)`

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Partial derivatives if ` (x,y) =ln (9xy^4 +14)`

Postby Galaxy » Tue 12 April, 2011 13:20

if (x,y) =ln (9xy^4 +14)
find partial `f_x` and partial derivative of `f_y`
How can I find the partial derivatives of a function f(x,y) ?
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Re: Partial derivatives if ` (x,y) =ln (9xy^4 +14)`

Postby Integr88 » Tue 12 April, 2011 13:27

if `(x,y) =ln (9xy^4 +14)`

first find the `f_x` which means take the derivatives of the function treating x as variable and everything else as constant. In this case y is assumed as constant.
we know that `dy/dxln(x^3)=1/x^3*3x^2` applying the same principle we can:
`f_x=1/(9xy^4 +14)*9y^4=(9y^4)/(9xy^4 +14)`

now we take the partial derivatives of `f_y` so we do the same but taking x a constant:
`f_y=1/(9xy^4 +14)*36xy^3=(36xy^3)/(9xy^4 +14)`
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