What is the d/(dt)((x)(ln(t))) ?

The d/(dt)((x)(ln(t))) is ln(t)(dx)/(dt)+x/t

What is the first d/(dt)((x)(ln(t))) ?

The first d/(dt)((x)(ln(t))) is ln(t)(dx)/(dt)+x/t

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

ln (t) \frac{d x}{d t} + \frac{x}{t}

Solution steps

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

Apply the Product Rule:

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

f = x, g = ln (t)

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

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

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

\frac{1}{t} x = \frac{x}{t}

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

a x + 2 a y + 2 b x + 4 b y

8 ab c + 2 + a c + 16 b

(x + 1)^{20}

x^{2} + 9 x + 2

cos (x) (24 0^{\circ})

What is the d/(dt)((x)(ln(t))) ?
The d/(dt)((x)(ln(t))) is ln(t)(dx)/(dt)+x/t
What is the first d/(dt)((x)(ln(t))) ?
The first d/(dt)((x)(ln(t))) is ln(t)(dx)/(dt)+x/t