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Drupady [299]
3 years ago
10

What is partial derivative of z=(2x+3y)^10 with respect to x,y?

Mathematics
2 answers:
Andru [333]3 years ago
8 0

Answer:

Step-by-step explanation:

Given that z is a function of x,y

z=(2x+3y)^{10}

Partially differentiate wrt x and y separately to get

\dfrac\partial{\partial x}(2x+3y)^{10}=10(2x+3y)^9\times2=20(2x+3y)^9\\\dfrac\partial{\partial y}(2x+3y)^{10}=10(2x+3y)^9\times3=30(2x+3y)^9

maw [93]3 years ago
3 0
Not sure if you mean to ask for the first order partial derivatives, one wrt x and the other wrt y, or the second order partial derivative, first wrt x then wrt y. I'll assume the former.

\dfrac\partial{\partial x}(2x+3y)^{10}=10(2x+3y)^9\times2=20(2x+3y)^9

\dfrac\partial{\partial y}(2x+3y)^{10}=10(2x+3y)^9\times3=30(2x+3y)^9

Or, if you actually did want the second order derivative,

\dfrac{\partial^2}{\partial y\partial x}(2x+3y)^{10}=\dfrac\partial{\partial y}\left[20(2x+3y)^9\right]=180(2x+3y)^8\times3=540(2x+3y)^8

and in case you meant the other way around, no need to compute that, as z_{xy}=z_{yx} by Schwarz' theorem (the partial derivatives are guaranteed to be continuous because z is a polynomial).
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