You can
put this solution on YOUR website!
.
The problem asks for you to take the derivative of the above expression. I presume that
the derivative is with respect to r and that v is a constant.
.
One term at a time. The product
is a constant so it is a multiplier of the derivative
of r. The rule that applies is that the derivative of
is
In this first term the exponent of r is 1. So you are taking the derivative of
which
the rule tells you in
and this simplifies to
.
Putting this all together for the first term, the derivative is
.
.
On to the second term. The most critical point here is to recognize that a positive
exponent in the denominator is equivalent to a negative exponent in the numerator.
Using this we can convert
to an equivalent form
.
.
Now we can apply the same technique as we did for the first term. The factor (2v) is
presumed to be a constant and therefore will be a multiplier of the derivative of
.
Again we use the rule that the derivative of
is
.
So the
derivative of
is
which simplifies to
.
Don't forget that this gets multiplied by the constant (2v) so that the derivative
for this second term is
. Multiplying this out results in:
.
and since a negative exponent in the numerator becomes a positive
exponent in the denominator, we could also write the derivative as:
.
.
.
Finally we combine the derivatives for the first and second terms to get:
.
.
and taking care of the signs for the second term concludes the effort by producing
the result:
.
.
Hope this helps you to see your way through the problem.
