What is the d/(dt)(5^{2t}) ?

The d/(dt)(5^{2t}) is 2ln(5)*25^t

What is the first d/(dt)(5^{2t}) ?

The first d/(dt)(5^{2t}) is 2ln(5)*25^t

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\frac{d}{d t} (5^{2 t})

2 ln (5) \cdot 2 5^{t}

Solution steps

\frac{d}{d t} (5^{2 t})

Simplify

5^{2 t} : 2 5^{t}

= \frac{d}{d t} (2 5^{t})

Apply the derivative exponent rule:

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

= 2 5^{t} ln (25)

Simplify

ln (25) : 2 ln (5)

= 2 ln (5) \cdot 2 5^{t}