Question

For \[f(x)=12x^{\frac{4}{3}}-6x^{\frac{1}{3}}\], which derivative is correct?

Options

• \[f'(x)=16x^{\frac{4}{3}}-\frac{2}{x^{\frac{1}{3}}}\]

• \[f'(x)=16x^{\frac{1}{3}}-\frac{2}{x^{\frac{2}{3}}}=\frac{2(8x-1)}{x^{\frac{2}{3}}}\]

• \[f'(x)=\frac{2(8x+1)}{x^{\frac{2}{3}}}\]

• \[f'(x)=12x^{\frac{1}{3}}-6x^{\frac{2}{3}}\]

Answer 1

Differentiating gives \[16x^{\frac{1}{3}}\] for the first term and \[-2/x^{\frac{2}{3}}\] for the second term. Combining them produces \[2(8x-1)/x^{\frac{2}{3}}\].