What is the d/(dt)((x)(t+sqrt(t))) ?

The d/(dt)((x)(t+sqrt(t))) is (dx)/(dt)(t+sqrt(t))+(1+1/(2sqrt(t)))x

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

The first d/(dt)((x)(t+sqrt(t))) is (dx)/(dt)(t+sqrt(t))+(1+1/(2sqrt(t)))x

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

\frac{d x}{d t} (t + t) + (1 + \frac{1}{2 t}) x

Solution steps

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

Apply the Product Rule:

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

f = x, g = t + t

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

\frac{d}{d t} (t + t) = 1 + \frac{1}{2 t}

= \frac{d x}{d t} (t + t) + (1 + \frac{1}{2 t}) x

(- a - x) (a + x)

(2 e^{2 t} + 2)^{2}

(e^{y} - y e^{y}) d y

\frac{( 1 - 3 t ) ( - 27 t e ^{- t} - 11 t - 8 )}{9}

(\frac{1}{24} sin (10 x) - \frac{5}{24} (sin (2 x))) cos (6 x)

What is the d/(dt)((x)(t+sqrt(t))) ?
The d/(dt)((x)(t+sqrt(t))) is (dx)/(dt)(t+sqrt(t))+(1+1/(2sqrt(t)))x
What is the first d/(dt)((x)(t+sqrt(t))) ?
The first d/(dt)((x)(t+sqrt(t))) is (dx)/(dt)(t+sqrt(t))+(1+1/(2sqrt(t)))x