What is the d/(dt)(e^{4(e^t-1)}) ?

The d/(dt)(e^{4(e^t-1)}) is 4e^{4(e^t-1)+t}

What is the first d/(dt)(e^{4(e^t-1)}) ?

The first d/(dt)(e^{4(e^t-1)}) is 4e^{4(e^t-1)+t}

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\frac{d}{d t} (e^{4 (e^{t} - 1)})

4 e^{4 (e^{t} - 1) + t}

Solution steps

\frac{d}{d t} (e^{4 (e^{t} - 1)})

Apply the chain rule:

e^{4 (e^{t} - 1)} \frac{d}{d t} (4 (e^{t} - 1))

= e^{4 (e^{t} - 1)} \frac{d}{d t} (4 (e^{t} - 1))

\frac{d}{d t} (4 (e^{t} - 1)) = 4 e^{t}

= e^{4 (e^{t} - 1)} \cdot 4 e^{t}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{4 (e^{t} - 1)} e^{t} = e^{4 (e^{t} - 1) + t}

= 4 e^{4 (e^{t} - 1) + t}

What is the d/(dt)(e^{4(e^t-1)}) ?
The d/(dt)(e^{4(e^t-1)}) is 4e^{4(e^t-1)+t}
What is the first d/(dt)(e^{4(e^t-1)}) ?
The first d/(dt)(e^{4(e^t-1)}) is 4e^{4(e^t-1)+t}