What is the derivative of g(t)=2log_{5}(t) ?

The derivative of g(t)=2log_{5}(t) is 2/(ln(5)t)

What is the first derivative of g(t)=2log_{5}(t) ?

The first derivative of g(t)=2log_{5}(t) is 2/(ln(5)t)

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derivative of

g (t) = 2 lo g_{5} (t)

\frac{2}{ln ( 5 ) t}

Solution steps

\frac{d}{d t} (2 lo g_{5} (t))

Take the constant out:

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

= 2 \frac{d}{d t} (lo g_{5} (t))

Apply the derivative log rule:

\frac{d}{d x} (lo g_{a} (x)) = \frac{1}{x ln ( a )}

= 2 \cdot \frac{1}{t ln ( 5 )}

Simplify

2 \cdot \frac{1}{t ln ( 5 )} : \frac{2}{ln ( 5 ) t}

= \frac{2}{ln ( 5 ) t}

What is the derivative of g(t)=2log_{5}(t) ?
The derivative of g(t)=2log_{5}(t) is 2/(ln(5)t)
What is the first derivative of g(t)=2log_{5}(t) ?
The first derivative of g(t)=2log_{5}(t) is 2/(ln(5)t)