What is the derivative of t*log_{10}(2t) ?

The derivative of t*log_{10}(2t) is log_{10}(2t)+1/(ln(10))

What is the first derivative of t*log_{10}(2t) ?

The first derivative of t*log_{10}(2t) is log_{10}(2t)+1/(ln(10))

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derivative of

t \cdot lo g_{10} (2 t)

lo g_{10} (2 t) + \frac{1}{ln ( 10 )}

Solution steps

\frac{d}{d t} (t lo g_{10} (2 t))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = lo g_{10} (2 t)

= \frac{d t}{d t} lo g_{10} (2 t) + \frac{d}{d t} (lo g_{10} (2 t)) t

\frac{d t}{d t} = 1

\frac{d}{d t} (lo g_{10} (2 t)) = \frac{1}{ln ( 10 ) t}

= 1 \cdot lo g_{10} (2 t) + \frac{1}{ln ( 10 ) t} t

Simplify

1 \cdot lo g_{10} (2 t) + \frac{1}{ln ( 10 ) t} t : lo g_{10} (2 t) + \frac{1}{ln ( 10 )}

= lo g_{10} (2 t) + \frac{1}{ln ( 10 )}

2 t^{2} e^{- t}

\frac{( x ^{2} + 1 )}{( 1 - x )}

\frac{d}{d t} (30 + 2 t)

y = 3 cos^{4} (x)

3 q^{2}

What is the derivative of t*log_{10}(2t) ?
The derivative of t*log_{10}(2t) is log_{10}(2t)+1/(ln(10))
What is the first derivative of t*log_{10}(2t) ?
The first derivative of t*log_{10}(2t) is log_{10}(2t)+1/(ln(10))