Question

Find second derivative of e2x + 5x​

Answer 1

Step-by-step explanation:

e2x + 5x

= d/dx (e2x +5x)

= (e2x (2) x2 /2 )+5x2/2

=e2x (x2)+ 5x2/2

Answer 2

Answer:

2nd derivative of $e^{2x}+5x$ is $4e^{2x}$

Step-by-step explanation:

let, $y=e^{2x}+5x$

To find: $\frac{\mathrm{d^2}y}{\mathrm{d}x^2}$

Consider,

$y=e^{2x}+5x$

Derivative both sides with respect to 'x'

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\mathrm{d}(e^{2x}+5x)}{\mathrm{d}x}=\frac{\mathrm{d}(e^{2x})}{\mathrm{d}x}+\frac{\mathrm{d}(5x)}{\mathrm{d}x}$

$=e^{2x}\times\frac{\mathrm{d}(2x)}{\mathrm{d}x}+5=2e^{2x}+5$

Now, again derivative with respect to 'x'

$\frac{\mathrm{d}(\frac{\mathrm{d}y}{\mathrm{d}x})}{\mathrm{d}x}=\frac{\mathrm{d}(2e^{2x}+5)}{\mathrm{d}x}$

$\frac{\mathrm{d^2}y}{\mathrm{d}x^2}=2\frac{\mathrm{d}(e^{2x})}{\mathrm{d}x}+\frac{\mathrm{d}(5)}{\mathrm{d}x}=2\times2e^{2x}+0=4e^{2x}$

Therefore, 2nd derivative of $e^{2x}+5x$ is $4e^{2x}$