The function f(x) = `e^(3x^2)`
f'(x) = `e^(3x^2)*6x`
f''(x) = `e^(3x^2)*6x*6x + e^(3x^2)*6`
=> `36x^2*e^(3x^2) + 6*(e^(3x^2))`
=> `(36x^2 + 6)*e^(3x^2)`
f'''(x) = `(36x^2 + 6)*e^(3x^2)*6x + 72x*e^(3x^2)`
=> `e^(3x^2)*(216x^3 + 108x)`
`f'(x) - f''(x) - f'''(x)`
=> `e^(3x^2)*6x - (36x^2 + 6)*e^(3x^2) - (e^(3x^2)*(216x^3 + 108x)`
=> `e^(3x^2)*(6x -...
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The function f(x) = `e^(3x^2)`
f'(x) = `e^(3x^2)*6x`
f''(x) = `e^(3x^2)*6x*6x + e^(3x^2)*6`
=> `36x^2*e^(3x^2) + 6*(e^(3x^2))`
=> `(36x^2 + 6)*e^(3x^2)`
f'''(x) = `(36x^2 + 6)*e^(3x^2)*6x + 72x*e^(3x^2)`
=> `e^(3x^2)*(216x^3 + 108x)`
`f'(x) - f''(x) - f'''(x)`
=> `e^(3x^2)*6x - (36x^2 + 6)*e^(3x^2) - (e^(3x^2)*(216x^3 + 108x)`
=> `e^(3x^2)*(6x - 36x^2 - 6 - 216x^3 - 108x)`
=> `e^(3x^2)*(-216x^3 - 36x^2 - 102x - 6)`
The expression for `f'(x) - f''(x) - f'''(x) = e^(3x^2)*(-216x^3 - 36x^2 - 102x - 6)`