What is the derivative of 640(1.06)^t ?

The derivative of 640(1.06)^t is 37.29210…*1.06^t

What is the first derivative of 640(1.06)^t ?

The first derivative of 640(1.06)^t is 37.29210…*1.06^t

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derivative of

640 (1.06)^{t}

37.29210 \dots \cdot 1.0 6^{t}

Solution steps

\frac{d}{d t} (640 \cdot 1.0 6^{t})

Take the constant out:

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

= 640 \frac{d}{d t} (1.0 6^{t})

Apply the derivative exponent rule:

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

= 640 \cdot 1.0 6^{t} ln (1.06)

Simplify

640 \cdot 1.0 6^{t} ln (1.06) : 37.29210 \dots \cdot 1.0 6^{t}

= 37.29210 \dots \cdot 1.0 6^{t}

What is the derivative of 640(1.06)^t ?
The derivative of 640(1.06)^t is 37.29210…*1.06^t
What is the first derivative of 640(1.06)^t ?
The first derivative of 640(1.06)^t is 37.29210…*1.06^t