Exercise 258Calculus › Multivariable calculus › Partial derivativesHigh schoolAdded 3 Nov 2026

First partial derivatives

#partial derivatives#definition#computation

Statement

Let $f(x,y)=x^2y+3xy^2-2x+5$ . Compute $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$ .

Hint

Differentiate with respect to one variable, treating the other as a constant.

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With respect to $x$ .
$\frac{\partial f}{\partial x}=2xy+3y^2-2.$

With respect to $y$ .
$\frac{\partial f}{\partial y}=x^2+6xy.$

Conclusion. The two partial derivatives are as above.