Question

differentiate the following

Answer 1

[0010001111]... Hello User... [1001010101]
Here's your answer...

Here, two functions are in division.
The quotient rule says that...
$y = \frac{f(x)}{g(x)} \\ then \: \\ \frac{dy}{dx} = \frac{g(x) \frac{d}{dx}f(x) - f(x) \frac{d}{dx} g(x) }{ {(g(x))}^{2} }$
$y = \frac{4 {x}^{3} }{ {e}^{x} } \\ \frac{dy}{dx} = \frac{ {e}^{x} \times 4 \times 3 {x}^{2} - 4 {x}^{3} \times {e}^{x} }{ {( {e}^{x}) }^{2} } \\ = \frac{ {e}^{x}(12 {x}^{2} - 4 {x}^{3} ) }{ {( {e}^{x} )}^{2} } \\ = \frac{12 {x}^{2} - 4 {x}^{3} }{ {e}^{x} }$
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