Mathematics · University
Evaluate a partial derivative · formula reference
Hold the other independent variable fixed while differentiating.
Formula
Hold the other independent variable fixed while differentiating.
∂(ax²y + by³)/∂x = 2axy
Worked example
For f(x,y) = 4x²y + 6y³, find ∂f/∂x at (-4, 1). Round the final result to 4 decimal places if needed.
Treat y as constant. The second term has zero x derivative, leaving 8xy. Substitute the point.
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Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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