What is the derivative of 5tln(t) ?

The derivative of 5tln(t) is 5(ln(t)+1)

What is the first derivative of 5tln(t) ?

The first derivative of 5tln(t) is 5(ln(t)+1)

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derivative of

5 t ln (t)

5 (ln (t) + 1)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = t, g = ln (t)

= 5 (\frac{d t}{d t} ln (t) + \frac{d}{d t} (ln (t)) t)

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

\frac{d}{d t} (ln (t)) = \frac{1}{t}

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

Simplify

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

= 5 (ln (t) + 1)

\int_{0}^{b} \frac{1}{16 - x ^{2}} d x

\frac{s}{s ^{2} + 2 s + 1}

\frac{d}{d x} (co tan (x) - tan (x))

\int \frac{x ^{2} - 2 x}{x} d x

What is the derivative of 5tln(t) ?
The derivative of 5tln(t) is 5(ln(t)+1)
What is the first derivative of 5tln(t) ?
The first derivative of 5tln(t) is 5(ln(t)+1)