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Popular >

d/(du)((t)(ln(t^2)+2ln(t)+2))

Solution

\frac{d}{d u} ((u) (ln (u^{2}) + 2 ln (u) + 2))

Solution

4 ln (u) + 6

Solution steps

\frac{d}{d u} ((u) (ln (u^{2}) + 2 ln (u) + 2))

Simplify

(u) (ln (u^{2}) + 2 ln (u) + 2) : u (ln (u^{4}) + 2)

= \frac{d}{d u} (u (ln (u^{4}) + 2))

Apply the Product Rule:

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

f = u, g = ln (u^{4}) + 2

= \frac{d u}{d u} (ln (u^{4}) + 2) + \frac{d}{d u} (ln (u^{4}) + 2) u

\frac{d u}{d u} = 1

\frac{d}{d u} (ln (u^{4}) + 2) = \frac{4}{u}

= 1 \cdot (ln (u^{4}) + 2) + \frac{4}{u} u

Simplify

1 \cdot (ln (u^{4}) + 2) + \frac{4}{u} u : 4 ln (u) + 6

= 4 ln (u) + 6

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Frequently Asked Questions (FAQ)

What is the d/(du)((t)(ln(t^2)+2ln(t)+2)) ?
The d/(du)((t)(ln(t^2)+2ln(t)+2)) is 4ln(u)+6
What is the first d/(du)((t)(ln(t^2)+2ln(t)+2)) ?
The first d/(du)((t)(ln(t^2)+2ln(t)+2)) is 4ln(u)+6