Question

Find second derivative of e2x + 5x.

Answer 1

2x+5x=7x
Because x is common in both so just do direct addition

Answer 2

it is given that function, f(x) = $e^{2x}+5x$

• concept : differentiation of f(x)ⁿ = nf(x)^{n-1} × df(x)/dx ,
• differentiation of e^f(x) = e^f(x) × df(x)/dx

now differentiating given function, f(x) with respect to x,

i.e., df(x)/dx = d(e^{2x}+5x)/dx = e^{2x} × d(2x)/dx +5

= 2e^{2x} + 5

again, differentiating with respect to x,

d²f(x)/dx² = 2 × 2e^{2x} + d(5)/dx= 4e^{2x}

[ as we know, differentiation of constant term is zero. that's why, d(5)/dx = 0 ]

hence, second derivative of e^{2x}+5x= 4e^{2x}