Second derivative of y=2x^ (1/5) + 3

d²y/dx² = - 8/25 (x) ^ (-9/5)

Step-by-step explanation:

y = 2 (x) ^ (1/5) + 3

Use power rule:

dy/dx = 2 (1/5) (x) ^ (1/5 - 1)

dy/dx = 2/5 (x) ^ (-4/5)

Use power rule again:

d²y/dx² = 2/5 (-4/5) (x) ^ (-4/5 - 1)

d²y/dx² = - 8/25 (x) ^ (-9/5)