Y=a^2x prove that d^2y/dx^2 =(2loga)^2 y?

$y=a^{2x}$

apply log on both sides

$\log y=2x\times \log a$

$differentiate\; both \;sides$

$\frac{1}{y}\times \frac{\mathrm{d y} }{\mathrm{d} x}=2\times \log a$

$\frac{\mathrm{d y} }{\mathrm{d} x}=2\times \log a \times y................eq(1)$

again differentiate both sides

$\frac{\mathrm{d^2} y}{\mathrm{d} x^2}=2\times \log a \times \frac{\mathrm{d}y }{\mathrm{d} x}$

using equation (1)

$\frac{\mathrm{d^2} y}{\mathrm{d} x^2}=2\times \log a \times 2\times \log a \times y$

$\frac{\mathrm{d^2} y}{\mathrm{d} x^2}=(2\times \log a)^2 \times y$

Hence proved

Most Viewed Questions

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-