Find the first partial derivatives of the following functions. f(x,y)=4x^{3}y^{2}+3x^{2}y^{3}+10

aortiH

aortiH

Answered question

2021-05-03

Find the first partial derivatives of the following functions.
f(x,y)=4x3y2+3x2y3+10

Answer & Explanation

liingliing8

liingliing8

Skilled2021-05-04Added 95 answers

Step 1
Given, f(x,y)=4x3y2+3x2y3+10
The partial derivative of f(x,y) with respect to x is,
f(x,y)=x(4x3y2+3x2y3+10)
=x(4x3y2)+x(3x2y3+10)
=12y2x2+y3x+0
=12y2x2+y3x
Step 2
Similarly,
The partial derivative of f(x,y) with respect to y is,
f(x,y)=y(4x3y2+3x2y3+10)
=y(3x2y3)+y(10)
=8x3y+9x2y2+0
=8x3y+9x2y2
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-20Added 2605 answers

Answer is given below (on video)

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