Answer: The second derivative would be
[tex]f''(x)=5e^{-x}-50e^{-5x}[/tex]
Step-by-step explanation:
Since we have given that
[tex]f(x)=5e^{-x}-2e^{-5x}[/tex]
We will find the first derivative w.r.t. 'x'.
So, it becomes,
[tex]f'(x)=-5e^{-x}+10e^{-5x}[/tex]
Then, we will find the second derivative w.r.t 'x'.[tex]f''(x)=5e^{-x}+10\times -5e^{-5x}\\\\f''(x)=5e^{-x}-50e^{-5x}[/tex]
Hence, the second derivative would be
[tex]f''(x)=5e^{-x}-50e^{-5x}[/tex]
