"Find the first partial derivatives of the following..." was answered by our community

ringearV

Answered question

2021-02-22

Find the first partial derivatives of the following functions.

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

SabadisO

Skilled2021-02-24Added 108 answers

Step 1
Obtain the first partial derivative of f with respect to x as shown below:

\frac{\partial f}{\partial x} = \frac{\partial}{\partial x} (e^{x^{2} y})

= e^{x^{2} y} \cdot \frac{\partial}{\partial x} (x^{2} y)

= e^{x^{2} y} \cdot (2 x y)

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

Step 2
Obtain the first partial derivative of f with respect to y as shown below:

\frac{\partial f}{\partial y} = \frac{\partial}{\partial y} (e^{x^{2} y})

= e^{x^{2} y} \cdot \frac{\partial}{\partial y} (x^{2} y)

= e^{x^{2} y} \cdot (x^{2})

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

Jeffrey Jordon

Expert2021-12-21Added 2605 answers

Answer is given below (on video)

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