Compute the given partial derivatives. f(x,y)=3x2y+4x3y2−7xy5,fx(1,2)

Tiffany Russell

Tiffany Russell

Answered

2022-01-14

Compute the given partial derivatives.
f(x,y)=3x2y+4x3y27xy5,fx(1,2)

Answer & Explanation

eskalopit

eskalopit

Expert

2022-01-15Added 31 answers

Step 1
Given,
f(x,y)=3x2y+4x3y27xy5,fx(1,2)
The objective is to determine the partial derivatives fx of the given function at given point.
For partial differentiation, differentiate the given function with respect to x, taking y as a constant.
Step 2
fx=x(3x2y+4x3y27xy5)
=x(3x2y)+x(4x3y2)x(7xy5)
=6yx+12y2x27y5
Thus, the value of fx at (1,2) is,
fx(1,2)=6yx+12y2x27y5
=6(2)(1)+12(2)2(1)27(2)5
=6(2)(1)+124(1)27(2)5
=12+12*4*1-7*32
=12+48-224
=-164

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