Determine d^2y/dx^2 for
y=(5x^5+7)^4
just use the chain rule
y' = 4(5x^5+7)^3 (25x^4)
= 100x^4 (5x^5+7)^3
Now again, also using the product rule
y" = 400x^3 (5x+7)^3 + 100x^4 * 3(5x^5+7)^2 (25x)
= 100x^3 (5x^5+7)^2 (95x^5+28)
y=(5x^5+7)^4
y' = 4(5x^5+7)^3 (25x^4)
= 100x^4 (5x^5+7)^3
Now again, also using the product rule
y" = 400x^3 (5x+7)^3 + 100x^4 * 3(5x^5+7)^2 (25x)
= 100x^3 (5x^5+7)^2 (95x^5+28)