another partial derivative

**el123** · September 16th 2009, 10:20 PM

$3x^2\ln(1-xy)$

i want to differentiate with respect to y.

So.
$[(0)(\ln(1-xy)]+[(3x^2)(-x)]$

which is $-3x^3$

Is that correct?

**seld** · September 16th 2009, 10:49 PM

again you're running into this same problem where you want to do a partial derivative in terms of y, but you're not holding x as a constant.

what type of function of y are you needing to differentiate (ie. polynomial, quotient etc.)

**redsoxfan325** · September 16th 2009, 11:03 PM

Originally Posted by el123

$3x^2\ln(1-xy)$

i want to differentiate with respect to y.

So.
$[(0)(\ln(1-xy)]+[(3x^2)(-x)]$

which is $-3x^3$

Is that correct?

Just treat $x$ like a number. $3x^2$ and $x$ are just constants.

If you were derivating $c_1\ln(1-c_2 y)$ , what would you get? You'd get $\frac{c_1}{1-c_2 y}\cdot -c_2$ . Just extend that notion to this problem.