Question

Prove that the derivative of `(e^(4x)/4-xe^(4x) ) = pxe^(4x)` and find `p`?

Answer 1

`p=-4`

Explanation:

Differentiating wrt `x` and applying the product rule, and chain rule we get:

`d/dx (e^(4x)/4-xe^(4x) ) = d/dx (e^(4x)/4) - x(d/dx e^(4x) ) - (d/dx x)(e^(4x) )`

`" " = d/dx ((4e^(4x))/4) - x(4e^(4x) ) - (1)(e^(4x) )`

`" " = e^(4x) - 4xe^(4x) - e^(4x )`

`" " = - 4xe^(4x)`

`" " = pxe^(4x)`, where `p=-4`