Find the partial derivative of z with respect to x if

$\displaystyle u = x^4y^3 $

and

$\displaystyle y = 7+4x^4$

Would the answer be

$\displaystyle f_x= 24x^3y^3+16x^3$

or have i done it wrong?

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- Sep 17th 2009, 01:21 AMel123Partial Derivative question.
Find the partial derivative of z with respect to x if

$\displaystyle u = x^4y^3 $

and

$\displaystyle y = 7+4x^4$

Would the answer be

$\displaystyle f_x= 24x^3y^3+16x^3$

or have i done it wrong? - Sep 17th 2009, 03:02 AMtom@ballooncalculus
Whole question please!

Total derivative of u with respect to x is the bottom row here...

http://www.ballooncalculus.org/asy/diffProd/rightY.png

... bearing some resemblance to your version. As always,

http://www.ballooncalculus.org/asy/chain.png

... is the chain rule, and...

http://www.ballooncalculus.org/asy/prod.png

... the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (which is the inner function of the composite and hence subject to the chain rule).

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