Hi. I need help with these questions (see image) Please show workings.

Question : Find the derivative with respect to x of each of the following:
(see image)

see explanation

Step-by-step explanation:

Note that x = lnx ( natural logarithm)

Using the standard derivatives

(lnx ) = , ( x ) =

Using the chain rule

Given y = f(g(x)) , then

= f'(g(x))) × g'(x) ← chain rule

(c)

y = (x² - 2) then

=  × (x² - 2)

    = × 2x

    =

(d)

y = ln( )

= × ( )

   = x × -

   = x ×

   = -

step-by-step explanation:

we can use this expression to calculate the energy gain as a particle moves with a field or the energy loss as it moves against it. (note that it is also used to define the electron-volt, a unit of energy equal to that gained by an electron as it falls through a pd of 1 v, i.e. w = 1 ev = 1.6 10-19 c 1 v = 1.6 10-19j).in fact this expression is really nothing more than the statement that potential is the potential energy per unit charge. in this case, v= w/qis simply stating that the change in potential energy(or work done) per unit charge is equal to the change in potential (or potential difference), v.student questions: uniform electric fields2electron beamcathode+5 kvanode0 v

the answer to question 1 is -8, 28.

step-by-step explanation: