Given that: y = 5x^3 + 7x + 3. What is dy/dx? What is d^2y/dx^2?
Firslty, the common rule when differentiating is nxm has the derivative of (n)(m)xm-1.
Therefore applying this rule to each individual component of the function:
dy/dx=(5)(3)x3-1+(7)(1)x1-1+(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)x2-1+7(0)
=30x
ME
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