What is the d/(dt)(8000(1.12)^t) ?

The d/(dt)(8000(1.12)^t) is 906.62948…*1.12^t

What is the first d/(dt)(8000(1.12)^t) ?

The first d/(dt)(8000(1.12)^t) is 906.62948…*1.12^t

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\frac{d}{d t} (8000 (1.12)^{t})

906.62948 \dots \cdot 1.1 2^{t}

Solution steps

\frac{d}{d t} (8000 (1.12)^{t})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8000 \frac{d}{d t} (1.1 2^{t})

Apply the derivative exponent rule:

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

= 8000 \cdot 1.1 2^{t} ln (1.12)

Simplify

8000 \cdot 1.1 2^{t} ln (1.12) : 906.62948 \dots \cdot 1.1 2^{t}

= 906.62948 \dots \cdot 1.1 2^{t}

What is the d/(dt)(8000(1.12)^t) ?
The d/(dt)(8000(1.12)^t) is 906.62948…*1.12^t
What is the first d/(dt)(8000(1.12)^t) ?
The first d/(dt)(8000(1.12)^t) is 906.62948…*1.12^t