Question

If y = e^3x then $\left( \frac { d ^ { 2 } y } { d x ^ { 2 } } \right)$ $\left( \frac{d^{2}x}{dy^{2}} \right)$ is

• A. 1
• B. e^–3x
• C. 3e^–3x
• D. –3e^–3x

Answer 1

Answer: (D)

–3e^–3x

Answer 2

y = e^3x then $\frac{dy}{dx}$ = 3e^3x

$\frac{d^{2}y}{dx}$ = 9.e^3x

$\frac{d^{2}x}{dy^{2}}$ = – $\frac{f´´(x)}{(f´(x))^{3}}$ = – $\frac{9e^{3x}}{(3.e^{3x})^{3}}$ = –$\frac{e^{3x}}{3.e^{9x}}$

⇒ $\frac{d^{2}y}{dx^{2}}$ × $\frac{d^{2}x}{dy^{2}}$ = 9.e^3x × $\left( \frac{–e^{3x}}{3.e^{9x}} \right)$ = – 3e^–3x