Partial derivatives

Task number: 3196

Calculate the partial derivative (with respect to all variables) of the following functions:

  • Variant 1

    \(x^2 + 4xy^3 + y^5\)

  • Variant 2

    \(x^{y^2}\)

  • Variant 3

    \((1 + x)^k(1 + y)^\ell(1 + z)^m\), where \(k, l, m\) are parameters.

  • Variant 4

    \(\ln(1+x)\ln(1+ y)\)

  • Variant 5

    \((1 + x)^{(1 + y)}\)

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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