Pre Calc Homework Find the Differential of the Function

Question

Please help I have no idea how to solve this problem and would beyond greatly appreciate detailed instructions.

Find the differential of the function.

f(x)=3x^5/6+7x^2/3

Answer 1

f'(x) = (5/6)3x^-1/6 + (2/3)7x^-1/3 = 5/2(x^1/6) + 14/(3x^1/3)

the derivative short cut rule is take the exponent and make it a part of the coefficient, then reduce the exponent by 1

6/7 - 1 = - 1/7 which can be 1/7 if you move the x term to the denominator

2/3 - 1 = -1/3 which can be 1/3 if you move the x term to the denominator

5/6 times 3 = 5/2

2/3 times 7 = 14/3