What is the solution for (df^{-1})/(dx)f(x)=3x^3-5x^2-2,x=1272 ?

The solution for (df^{-1})/(dx)f(x)=3x^3-5x^2-2,x=1272 is f(x)=e^{-(3x^4)/4+(5x^3)/3+2x-c_{1}}

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(df^{-1})/(dx)f(x)=3x^3-5x^2-2,x=1272

\frac{d f ^{- 1}}{d x} f (x) = 3 x^{3} - 5 x^{2} - 2, x = 1272

f (x) = e^{- \frac{3 x ^{4}}{4} + \frac{5 x ^{3}}{3} + 2 x - c_{1}}

Solution steps

\frac{d}{d x} (f (x)^{- 1}) f (x) = 3 x^{3} - 5 x^{2} - 2

Solve separable ODE:

f (x) = e^{- \frac{3 x ^{4}}{4} + \frac{5 x ^{3}}{3} + 2 x - c_{1}}

f (x) = e^{- \frac{3 x ^{4}}{4} + \frac{5 x ^{3}}{3} + 2 x - c_{1}}

\frac{1 + x}{1 + e ^{x}}

x = 8 y^{2}, x = 20 + 3 y^{2}

\frac{d}{d x} ((x^{2} + 5 x + 2)^{7})

\int x^{3} 64 - x^{2} d x

\int x 81 + x^{2} d x

What is the solution for (df^{-1})/(dx)f(x)=3x^3-5x^2-2,x=1272 ?
The solution for (df^{-1})/(dx)f(x)=3x^3-5x^2-2,x=1272 is f(x)=e^{-(3x^4)/4+(5x^3)/3+2x-c_{1}}