Question

If \[ (3y)^{2x}=5\left(2^{3x}\right), \] then \[ \left(\frac{dy}{dx}\right)_{x=1} = \]

• A. \(-\dfrac{\sqrt{10}\log 5}{3}\)
• B. \(-\dfrac{\sqrt{10}}{3}\)
• C. \(\dfrac{\sqrt{10}\log 5}{3}\)
• D. \(\dfrac{\sqrt{10}}{3}\)

Hint:

For equations of the form \(f(x,y)^{g(x)}=h(x)\), always use logarithmic differentiation. It converts exponents into products, making differentiation much easier.

Answer 1

The Correct Option is A