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Câu hỏi: Đạo hàm của hàm số $y={{\left( \dfrac{3}{2} \right)}^{x}}$ là
A. ${y}'=\dfrac{{{\left( \dfrac{3}{2} \right)}^{x}}}{\ln \dfrac{3}{2}}$.
B. ${y}'=\dfrac{{{\left( \dfrac{3}{2} \right)}^{x}}}{{{x}^{2}}}$.
C. ${y}'=\ln \dfrac{3}{2}.{{\left( \dfrac{3}{2} \right)}^{x}}$.
D. ${y}'=\dfrac{\ln \dfrac{3}{2}}{{{\left( \dfrac{3}{2} \right)}^{x}}}$.
A. ${y}'=\dfrac{{{\left( \dfrac{3}{2} \right)}^{x}}}{\ln \dfrac{3}{2}}$.
B. ${y}'=\dfrac{{{\left( \dfrac{3}{2} \right)}^{x}}}{{{x}^{2}}}$.
C. ${y}'=\ln \dfrac{3}{2}.{{\left( \dfrac{3}{2} \right)}^{x}}$.
D. ${y}'=\dfrac{\ln \dfrac{3}{2}}{{{\left( \dfrac{3}{2} \right)}^{x}}}$.
Ta có: ${{\left( {{a}^{x}} \right)}^{\prime }}={{a}^{x}}.\ln a\left( 1\ne a>0; x\in \mathbb{R} \right)$. Do đó: ${y}'=\ln \dfrac{3}{2}.{{\left( \dfrac{3}{2} \right)}^{x}}$.
Đáp án C.