$x$ এর সাপেক্ষে $x^{2} \log _{a} x+7 e^{x} \cdot \cos x$ এর অন্তরক সহগ নিচের কোনটি ?

Solve:

$\begin{array}{l} x^{2} \log _{a} x+7 e^{x} \cdot \cos x \\ \frac{d}{d x}\left(x^{2} \log _{a} x+7 e^{x} \cos x\right)=x^{2} \frac{d}{d x}\left(\log _{a} x\right) \\ +\log _{a} x \frac{d}{d x}\left(x^{2}\right)+7\left\{e^{x} \frac{d}{d x}(\cos x)+\right. \\ \left.\cos x \frac{d}{d x}\left(e^{x}\right)\right\} \\ =x^{2} \frac{1}{x \ln a}+\log _{a} x(2 x)+ \end{array}$

$\begin{array}{r} 7\left\{e^{x}(-\sin x)+\cos x \cdot e^{x}\right\} \\ =x\left(\frac{1}{\ln a}+2 \log _{a} x\right)+7 e^{x}(\cos x-\sin x) \end{array}$