What is the solution for f^'(x)=7e^{-e}-5e^{-7x} ?

The solution for f^'(x)=7e^{-e}-5e^{-7x} is f(x)= 7/(e^e)x+5/7 e^{-7x}+c_{1}

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f^'(x)=7e^{-e}-5e^{-7x}

f^{^{'}} (x) = 7 e^{- e} - 5 e^{- 7 x}

f (x) = \frac{7}{e ^{e}} x + \frac{5}{7} e^{- 7 x} + c_{1}

Solution steps

f^{'} (x) = 7 e^{- e} - 5 e^{- 7 x}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (x) = \int 7 e^{- e} - 5 e^{- 7 x} d x

\int 7 e^{- e} - 5 e^{- 7 x} d x = \frac{7}{e ^{e}} x + \frac{5}{7} e^{- 7 x} + c_{1}

f (x) = \frac{7}{e ^{e}} x + \frac{5}{7} e^{- 7 x} + c_{1}

x \to 0 + lim (\frac{3}{1 + e ^{\frac{1}{x}}})

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What is the solution for f^'(x)=7e^{-e}-5e^{-7x} ?
The solution for f^'(x)=7e^{-e}-5e^{-7x} is f(x)= 7/(e^e)x+5/7 e^{-7x}+c_{1}