Calculate the first, second, and third derivatives of 𝑦(𝑥)=6√x.

Question

𝑦′(𝑥)=

𝑦″(𝑥)=

𝑦‴(𝑥)=

Answer 1

This is repeated application of the power rule, which you might recall is:

d/dx (a*x^b) = a * b * x^b-1

In other words, multiply the coefficient by the value of the exponent, then subtract one from the exponent.

So y'(x) = 3x^-1/2

Can you keep applying the rule to get the second and third derivatives?