Expert Answer to "Find f×(x,y) and fxy(x,y) derivatives for the following" - Plainmath

Francisca Rodden

Answered question

2021-12-07

Find

f_{\times} (x, y) and f_{x y} (x, y)

derivatives for the following function

z = f (x, y) = e^{x^{2} + y^{2}}

Answer & Explanation

aquariump9

Beginner2021-12-08Added 40 answers

Step 1
Consider the given function

z = f (x, y) = e^{x^{2} + y^{2}}

....(1)
Differentiating (1) partially with respect to x we get

f_{x} (x, y) = e^{x^{2} + y^{2}} (2 x + 0)

...(2)

= 2 x e^{x^{2} + y^{2}}

Again differentiating with respect to x we get

f_{\times} (x, y) = 2 e^{x^{2} + y^{2}} + 2 x e^{x^{2} + y^{2}} (2 x)

= e^{x^{2} + y^{2}} (2 + 4 x^{2})

Step 2
Differentiating (2) with respect to y we get

f_{x y} (x, y) = 2 x e^{x^{2} + y^{2}} (2 y)

= 4 x y e^{x^{2} + y^{2}}

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