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Question

What is the derivative of xy3?


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Solution

Step 1: Calculating differentiate the function xy3 with respect to x

Derivative formula:

Power rule:dxadx=axa-1

Composite function: ddxfgx=f'gx·g'x

Product rule: ddxuv=udvdx+vdudx

Differentiate the function xy3 with respect to x, we get

ddxxy3=xdy3dx+y3dxdx

ddxxy3=x3y2dydx+y31

ddxxy3=3xy2dydx+y3

Step 2: Calculating differentiate the function xy3 with respect to y

Differentiate the function xy3 with respect to y, we get

ddyxy3=xdy3dy+y3dxdy

ddyxy3=x3y2+y3dxdy

ddyxy3=3xy2+y3dxdy

Hence, the derivative of xy3 with respect to x is 3xy2dydx+y3 and the derivative of xy3 with respect to y is 3xy2+y3dxdy.


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