Derivatives involving exponential and logarithmic functions

A. Find the derivative of the function (1-6). 

1. (a) \(f(x)=e^{2x-7} \)   (b) \( f(x)=\ln (2x+7) \)   (c) \( f(x)=x^2e^{3x}\)   solution

2. (a) \( f(x)=6(\ln (x))^{5/2} \)  (b) \(\displaystyle{f(x) = \frac{\ln x}{e^x - x}}\)   solution

3. (a) \(\displaystyle{f(x) = e^{-5x} }\)   (b) \(\displaystyle{f(x) = (2+\ln x)^5 }\)   (c)\(\displaystyle{f(x) = \ln (5x^2 -x+3) }\)    solution

4. (a) \(\displaystyle{f(x) = \ln \frac{2x}{x-1} }\)     (b) \(\displaystyle{f(x) = \ln (x^2 e^x) }\)   solution

5. (a) \(\displaystyle{f(x) = x^3 \, e^{x^9-2} }\)   (b) \(\displaystyle{f(x) = 7^{x}\, \ln(6x+10)}\)  solution

6. (a) \(\displaystyle {f(x)=(x+5)e^x}\)   (b) \(\displaystyle{ f(x)=\frac{e^{2x}-1}{\ln (x)+3} }\)    solution

B. If \( f(x) = \frac{\ln x }{x^2} \), find \(f'(1)\).    solution