First, the derivative of f+ g is the derivative of f plus the derivative of g and the derivtive of a constant, 45, is 0 so this is the same as the derivative of just \(\displaystyle -45e^{-\frac{ln(90)x}{2}}\)
Second, the derivative of a constant, -45, times f is that constant times the derivative of f so that is -45 times the derivative of \(\displaystyle e^{-\frac{ln(90)x}{2}}\).
Third the derivative of e to the f power is e to the f power times the derivative of f so we have \(\displaystyle -45e^{-\frac{ln(90x)}{2}}\) times the derivative of \(\displaystyle \frac{ln(90)x}{2}= \left(\frac{ln(90)}{2}\right)x\).
And that, again, is a constant times x so its derivative is just \(\displaystyle -\frac{ln(90)}{2}\).
So the derivative of \(\displaystyle -45e^{-\frac{ln(90)x}{2}}+ 45\) is
\(\displaystyle (-45)\left(-\frac{ln(90)}{2}\right)e^{-\frac{ln(90)x}{2}}\)