Exercise 257Calculus › Multivariable calculus › Partial derivativesHigh schoolAdded 3 Nov 2026

Evaluating partial derivatives at a point

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Statement

Let $f(x,y)=e^{xy}+\ln(1+x^2)$ . Compute $\frac{\partial f}{\partial x}(0,1)$ and $\frac{\partial f}{\partial y}(0,1)$ .

Hint

Compute the partial derivatives, then substitute $(x,y)=(0,1)$ .

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Partial derivatives.
$\frac{\partial f}{\partial x}=ye^{xy}+\frac{2x}{1+x^2},\qquad \frac{\partial f}{\partial y}=xe^{xy}.$

At $(0,1)$ . $\frac{\partial f}{\partial x}(0,1)=1\cdot1+0=1$ , $\frac{\partial f}{\partial y}(0,1)=0$ .

Conclusion. The values are $1$ and $0$ .