It is given that $y=2{{e}^{-2x}}+{{e}^{-3x}}$. Find the first, the second and the third deriv

Question

It is given that $y=2{{e}^{-2x}}+{{e}^{-3x}}$. Find the first, the second and the third derivatives. Hence, find an expression for $\frac{{{\mathrm{d}}^{n}}y}{\mathrm{d}{{x}^{n}}}$ in terms of $n$ and $x$.

Accepted Answer

$y'=-4\mathrm e^{-2x}-3\mathrm e^{-3x}$, $y''=8\mathrm e^{-2x}+9\mathrm e^{-3x}$, $y'''=-16\mathrm e^{-2x}-27\mathrm e^{-3x}$. For $n\ge1$, $y^{(n)}=2(-2)^n\mathrm e^{-2x}+(-3)^n\mathrm e^{-3x}$.

Techniques of Differentiation - Second and Higher Derivatives

Techniques of Differentiation - Second and Higher Derivatives

Solution:

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