Given that: y = 5x^3 + 7x + 3. What is dy/dx? What is d^2y/dx^2?

Firslty, the common rule when differentiating is nx^m has the derivative of (n)(m)x^m-1.

Therefore applying this rule to each individual component of the function:

dy/dx=(5)(3)x^3-1+(7)(1)x^1-1+(3)(0)

=(15)x²+7x⁰+0

=15x²+7

To find out d²y/dx² we simply follow this rule again for the first derivative of the function (dy/dx).

d²y/dx²=(15)(2)x^2-1+7(0)

=30x