What is the first d/(dt)(e^{kt}) ?

The first d/(dt)(e^{kt}) is e^{kt}k

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d/(dt)(e^{kt})

\frac{d}{d t} (e^{k t})

e^{k t} k

Solution steps

\frac{d}{d t} (e^{k t})

Apply the chain rule:

e^{k t} \frac{d}{d t} (k t)

= e^{k t} \frac{d}{d t} (k t)

\frac{d}{d t} (k t) = k

= e^{k t} k

(2 x^{2} y) (3 x^{5} y)

6.7 \cdot 1 0^{- 5}

1 + x^{2} \cdot x^{2} - 1