Question

Whst is the second derivative of y=a (e^2x) + b (e^-mx)?

Answer 1

$\bold{Answer :}$

Given that,

y = a (e²ˣ) + b (e⁻ᵐˣ)

∴ differentiating with respect to x, we get

dy/dx = a d/dx (e²ˣ) + b d/dx (e⁻ᵐˣ)

or, dy/dx = 2a (e²ˣ) - bm (e⁻ᵐˣ) ...(i)

Again differentiating both sides of (i), we get

d²y/dx² = 2a d/dx (e²ˣ) - bm d/dx (e⁻ᵐˣ)

= 4a (e²ˣ) + bm² (e⁻ᵐˣ),

which is the required value.

Here, d/dx (eᵐˣ) = m (eᵐˣ)

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