What is the d/(dt)((x)(10x+30t)) ?

The d/(dt)((x)(10x+30t)) is 30t(dx)/(dt)+20x(dx)/(dt)+30x

What is the first d/(dt)((x)(10x+30t)) ?

The first d/(dt)((x)(10x+30t)) is 30t(dx)/(dt)+20x(dx)/(dt)+30x

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\frac{d}{d t} ((x) (10 x + 30 t))

30 t \frac{d x}{d t} + 20 x \frac{d x}{d t} + 30 x

Solution steps

\frac{d}{d t} ((x) (10 x + 30 t))

Apply the Product Rule:

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

f = x, g = 10 x + 30 t

= \frac{d x}{d t} (10 x + 30 t) + \frac{d}{d t} (10 x + 30 t) x

\frac{d}{d t} (10 x + 30 t) = 10 \frac{d x}{d t} + 30

= \frac{d x}{d t} (10 x + 30 t) + (10 \frac{d x}{d t} + 30) x

Simplify

\frac{d x}{d t} (10 x + 30 t) + (10 \frac{d x}{d t} + 30) x : 30 t \frac{d x}{d t} + 20 x \frac{d x}{d t} + 30 x

= 30 t \frac{d x}{d t} + 20 x \frac{d x}{d t} + 30 x

3 (4 y = 3 - 5 y + 7)

f (x) (3 x - 1)^{2} e^{2 x + 1}

(4 x^{5} - 5) d x

sin (2 x - 9 0^{\circ})

e^{(x - 2)}

What is the d/(dt)((x)(10x+30t)) ?
The d/(dt)((x)(10x+30t)) is 30t(dx)/(dt)+20x(dx)/(dt)+30x
What is the first d/(dt)((x)(10x+30t)) ?
The first d/(dt)((x)(10x+30t)) is 30t(dx)/(dt)+20x(dx)/(dt)+30x