Question

How do you simply from this?

Answer 1

\[(-1/2) * ((\cos x) x^(3/2) / (3/2) )\]

Answer 2

to

Answer 3

\[-1/3 x^(3/2) \cos(x) \]

Answer 4

I rewrite the expression with a bigger font for clarity:
\[\Large (-\frac{ 1 }{ 2 }) \times \frac{ \cos(x) \times x ^{\frac{ 3 }{ 2 }}}{ \frac{ 3 }{2 } }\]
Everything remains the same except (-1/2) is divided by (3/2) which is the same as multiplying by its reciprocal: \[\Large \frac{ -\frac{ 1 }{ 2 } }{ \frac{ 3 }{ 2 }} = -\frac{ 1 }{ 2 } \times \frac{ 2 }{ 3 } = -\frac{ 1 }{ 3 }\]So you now have:\[\Large -\frac{ 1 }{ 3 }x ^{\frac{ 3 }{ 2 }}\cos(x)\]