Derivatives of Exponentials I

\frac{d}{d x} e^{-4 x^{3} - 5 x^{2} - 4 x}

=

\frac{d}{d x} e^{u}

=

\frac{d}{d u} (e^{u}) \frac{d u}{d x}

=

e^{u} (-12 x^{2} - 10 x - 4)

=

e^{-4 x^{3} - 5 x^{2} - 4 x} (-12 x^{2} - 10 x - 4)

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Copyright © Dayal D. Purohit, Ph.D.(Mathematics)