Differentiate a ^ x x x w.r.t. x.

Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability

1. \(\frac{\mathbf{a}^{\mathbf{x}}\left[\frac{\mathbf{5 i n} \mathbf{x}}{\mathbf{x}}+\sin \mathbf{x} \cdot \log \mathbf{a} \cdot \log \mathbf{x}-\log \mathbf{x} \cdot \cos \mathbf{x}\right]}{\sin ^{2} \mathbf{x}}\)
2. \(\frac{\mathbf{a}^{\mathbf{x}}\left(\frac{\sin \mathbf{x}}{\mathbf{x}}-\sin \mathbf{x} \cdot \log \mathbf{a} \cdot \log \mathbf{x}+\log \cos \mathbf{x}\right)}{\sin ^{2} \mathbf{x}}\)
3. \(\frac{\mathbf{a}^{\mathbf{x}}\left(\frac{\sin \mathbf{x}}{\mathbf{x}}+\sin \mathbf{x} \cdot \log \mathbf{a} \cdot \log \mathbf{x}+\log \cos \mathbf{x}\right)}{\sin ^{2} \mathbf{x}}\)
4. None of these

Answer

(A) a ^ x [ 5 i n x x + x a x - x x ] ^ 2 x

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