Derivatives of Exponentials I

\frac{d}{d x} e^{-6 x^{5} + 3 x^{4} - 3 x^{3} - 2 x^{2} + 5 x + 9}

=

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

=

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

=

e^{u} (-30 x^{4} + 12 x^{3} - 9 x^{2} - 4 x + 5)

=

e^{-6 x^{5} + 3 x^{4} - 3 x^{3} - 2 x^{2} + 5 x + 9} (-30 x^{4} + 12 x^{3} - 9 x^{2} - 4 x + 5)

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