Question

If $y=2^x \cdot 3^{2 x-1}$, then $\frac{d^2 y}{d x^2}$ is equal to

(A) $(\log 2)(\log 3)$

(B) $(\log 18)$

(C) $\left(\log 18^2\right) y^2$

(D) $(\log 18) y$

Answer 1

$\begin{array}{l}y=2^x \cdot 3^{2 x-1} \\\frac{d y}{d x}=2^x \cdot 3^{2 x-1} 2 \log 3+3^{2 x^2-1} \cdot 2^x \log 2 \\=2^x \cdot 3^{2 x-1} \log 18=y \log 18 \\\end{array}$

So, The correct option will be (D).