Finf the critical points of f(x,y)= e^xy +3

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2022-01-27

Finf the critical points of f(x,y)= e^xy +3 and use the second derivative test

Answer & Explanation

alenahelenash

alenahelenash

Expert2022-03-10Added 556 answers

f(x,y)=exy+3

Find the first derivative.

Since y3 is constant with respect to x, the derivative of exy3 with respect to x is y3ddx[ex].

f(x)=y3ddx(ex)

Differentiate using the Exponential Rule which states that ddx[ax] is a2ln(a) where a=e

f(x)=y3ex

Find the second derivative.

Since y3 is constant with respect to x, the derivative of exy3 with respect to x is y3ddx[ex].

f(x)=y3ddx(ex)

 Differentiate using the Exponential Rule which states that ddx[ax] is a2ln(a) where a=e

f(x)=y3ex

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