Question

Find dy/DX
y = 3ex
y = x2ex
y = ex/x3​

Answer 1

`a) (d)/(dx) (3e {}^(x) ) \\`

Recall the property

`(d)/(dx) [c * f(x)] = c * f'(x) \\`

`= 3 (d)/(dx) e {}^(x) = 3e {}^(x) \\`

`b.) \: \: (d)/(dx) (x {}^(2) e {}^(x) ) \\`

`= x {}^(2) * e {}^(x) +e {}^(x) * 2x \\`

`= e {}^(x) (x {}^(2) * 2x) \\`

`c.) \: \: (d)/(dx)( \frac{e {}^(x) }{x {}^(3) } ) \\`

`= \frac{x {}^(3) * e {}^(x) - e {}^(x) * {3x}^(2) }{ {x}^(6) } \\`

`= \frac{x {}^(2) {e}^(x) (x - 3) }{ {x}^(6) } \\`

`= \frac{ {e}^(x) (x - 3) }{ {x}^(4) } \\`