Question:medium

If \[ f(x)=\left(\log x\right)^{\sin x},\qquad x>e, \] then \(f'(\pi)=\)

Show Hint

For functions of the form \[ y=u(x)^{v(x)}, \] use logarithmic differentiation: \[ \boxed{\ln y=v\ln u.} \] Then differentiate implicitly and finally multiply by \(y\).
Updated On: Jul 18, 2026
  • \(\log \pi\)
  • \(-\log \pi\)
  • \(\log(\log \pi)\)
  • \(-\log(\log \pi)\)
Show Solution

The Correct Option is D

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