What is the d/(dt)(0.9^t) ?

The d/(dt)(0.9^t) is -0.10536…*0.9^t

What is the first d/(dt)(0.9^t) ?

The first d/(dt)(0.9^t) is -0.10536…*0.9^t

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\frac{d}{d t} (0. 9^{t})

- 0.10536 \dots \cdot 0. 9^{t}

Solution steps

\frac{d}{d t} (0. 9^{t})

Apply the derivative exponent rule:

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

= 0. 9^{t} ln (0.9)

Simplify

0. 9^{t} ln (0.9) : - 0.10536 \dots \cdot 0. 9^{t}

= - 0.10536 \dots \cdot 0. 9^{t}