need help math question

Question

if f(x)=3x^7-4/x^2+4 (3√x+1, find f'(x) and f''(x)

Answer 1

If f(x) is meant to equal 3x⁷ − 4x^-2 + 4(3x^0.5 + 1),

then f'(x) is constructed as 7(3x^7-1) − -2(4x^-2-1) + 4[0.5(3x^0.5-1)+ d(1)/dx].

This last "cleans up" to yield f'(x) as 21x⁶ + 8x^-3 + 6x^-0.5 + 0.

Now go from f'(x) to f''(x).

Write 21x⁶ + 8x^-3 + 6x^-0.5 + 0 and differentiate to

6(21x^6-1) + -3(8x^-3-1) + -0.5(6x^-0.5-1).

Reduce this last to gain f''(x) as 126x⁵ − 24x^-4 − 3x^-1.5.