Multiple choice general knowledge math & puzzles

d/dx(u^v) =

  1. (uv^v-1)dv/dx +(uv^v) du/dx

  2. (vu^v-1)du/dx +((Inu)u^v) dv/dx

  3. (uv^u-1)du/dv +((Inu)v^u) dx/dx

  4. (v^u-1)du/dv +((Inu)^u) dy/dx
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B Correct answer
Explanation

The derivative of a function in the form u^v is found using logarithmic differentiation or the identity u^v = e^(v ln u). The result is u^v * [v/u * du/dx + ln(u) * dv/dx], which rearranges to (v * u^(v-1))du/dx + (ln(u) * u^v)dv/dx.

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