Original
Starting with
{{MATH_126}}
we differentiate both sides of the
equation with respect to {{MATH_127}} to obtain
{{MATH_128}}
Applying the sum rule we get that
{{MATH_129}}
Let's examine each of these terms in turn. To start
{{MATH_130}}
On the other hand {{MATH_131}} is somewhat different. Here you assume that {{MATH_132}}, on some interval {{MATH_133}}, and hence by the chain rule
{{ENV_134}}
Considering the final term {{MATH_135}}, we assume that {{MATH_136}}, on some interval {{MATH_137}}. Hence
{{ENV_138}}
Putting this all together we are left with the equation
{{MATH_139}}
At this point, we solve for {{MATH_140}}. Write
{{ENV_141}}