What is the d/(dt)(ln(a+{v}(t)t)) ?

The d/(dt)(ln(a+{v}(t)t)) is (t d/(dt)({v}(t))+{v}(t))/(a+t{v)(t)}

What is the first d/(dt)(ln(a+{v}(t)t)) ?

The first d/(dt)(ln(a+{v}(t)t)) is (t d/(dt)({v}(t))+{v}(t))/(a+t{v)(t)}

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\frac{d}{d t} (ln (a + v (t) t))

\frac{t \frac{d}{d t} ( v ( t ) ) + v ( t )}{a + t v ( t )}

Solution steps

\frac{d}{d t} (ln (a + v (t) t))

Apply the chain rule:

\frac{1}{a + v ( t ) t} \frac{d}{d t} (a + v (t) t)

= \frac{1}{a + v ( t ) t} \frac{d}{d t} (a + v (t) t)

\frac{d}{d t} (a + v (t) t) = t \frac{d}{d t} (v (t)) + v (t)

= \frac{1}{a + v ( t ) t} (t \frac{d}{d t} (v (t)) + v (t))

Simplify

\frac{1}{a + v ( t ) t} (t \frac{d}{d t} (v (t)) + v (t)) : \frac{t \frac{d}{d t} ( v ( t ) ) + v ( t )}{a + t v ( t )}

= \frac{t \frac{d}{d t} ( v ( t ) ) + v ( t )}{a + t v ( t )}

\frac{d}{d x} ((- 1)^{n} x^{2 n})

y^{^{'}} = 0.5 y, y (2) = 100

x \to - 1 lim (\frac{∣ x + 1 ∣}{x + 1})

\int_{1}^{2} (2 x + 1) ln (x) d x

\int \frac{x ^{2} + 1}{x ^{3} + 3 x - 16} d x

What is the d/(dt)(ln(a+{v}(t)t)) ?
The d/(dt)(ln(a+{v}(t)t)) is (t d/(dt)({v}(t))+{v}(t))/(a+t{v)(t)}
What is the first d/(dt)(ln(a+{v}(t)t)) ?
The first d/(dt)(ln(a+{v}(t)t)) is (t d/(dt)({v}(t))+{v}(t))/(a+t{v)(t)}