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Compute the following partialsa) ∂/∂y (x2y3 + 2x3 ln(xy2))b) ∂/∂x (xy3e√(xy))c) ∂/∂y (y2sin(ylnx))

Question

Compute the following partials

a) ∂/∂y (x2y3 + 2x3 ln(xy2))

b) ∂/∂x (xy3e√(xy))

c) ∂/∂y (y2sin(ylnx))

check_circleAnswer
Step 1

(a) The partial derivative is  ∂/∂y (x2y3 + 2x3 ln(xy2).

Obtain the derivative as follows
1
(2xy)
(y2r In(xy2))=3xy +2r
By chain rule
4x3
-3x2y2
4x3
(x'y'+2x' In(xy')) = 3x'y'
Thus, the partial derivative
help_outline

Image Transcriptionclose

Obtain the derivative as follows 1 (2xy) (y2r In(xy2))=3xy +2r By chain rule 4x3 -3x2y2 4x3 (x'y'+2x' In(xy')) = 3x'y' Thus, the partial derivative

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Step 2

(b)

Tha partial derivative ∂/∂x (xy3...

Obtain the derivative as follows.
e
ax
(se)
ax
e
2x
+ev
( Product rule)
te
2
Thus, the partial derivative
xy'e
ax
2
help_outline

Image Transcriptionclose

Obtain the derivative as follows. e ax (se) ax e 2x +ev ( Product rule) te 2 Thus, the partial derivative xy'e ax 2

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Tagged in

Math

Calculus

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