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Mathematics · University

Evaluate a partial derivative

Hold the other independent variable fixed while differentiating.

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Method and conditions

Hold the other independent variable fixed while differentiating.

∂(ax²y + by³)/∂x = 2axy

Worked examples

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.

-32

For f(x,y) = 2x²y + 9y³, find ∂f/∂x at (-3, 6). Round the final result to 4 decimal places if needed.

Treat y as constant. The second term has zero x derivative, leaving 4xy. Substitute the point.

-72

Try it

  1. For f(x,y) = 2x²y + 8y³, find ∂f/∂x at (6, 8). Round the final result to 4 decimal places if needed.

  2. For f(x,y) = 6x²y + 3y³, find ∂f/∂x at (-3, 1). Round the final result to 4 decimal places if needed.

Check your work

Answers and marking notes
  1. 192

    Treat y as constant. The second term has zero x derivative, leaving 4xy. Substitute the point.

  2. -36

    Treat y as constant. The second term has zero x derivative, leaving 12xy. Substitute the point.

Further reading and review references

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