What is the d/(dt)((x)(2t+2t^3)) ?

The d/(dt)((x)(2t+2t^3)) is (dx)/(dt)(2t+2t^3)+(2+6t^2)x

What is the first d/(dt)((x)(2t+2t^3)) ?

The first d/(dt)((x)(2t+2t^3)) is (dx)/(dt)(2t+2t^3)+(2+6t^2)x

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\frac{d}{d t} ((x) (2 t + 2 t^{3}))

\frac{d x}{d t} (2 t + 2 t^{3}) + (2 + 6 t^{2}) x

Solution steps

\frac{d}{d t} ((x) (2 t + 2 t^{3}))

Apply the Product Rule:

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

f = x, g = 2 t + 2 t^{3}

= \frac{d x}{d t} (2 t + 2 t^{3}) + \frac{d}{d t} (2 t + 2 t^{3}) x

\frac{d}{d t} (2 t + 2 t^{3}) = 2 + 6 t^{2}

= \frac{d x}{d t} (2 t + 2 t^{3}) + (2 + 6 t^{2}) x

A (4, - 10) B (- 6, - 8)

\frac{6}{( 2 x + 7 ) ^{4}}

x - 2 (x + 10 = 12)

e^{2 x - x^{2}} (2 - 2 x) + 2 + 2 x

(3 x^{2} + 9 x - 4)^{5}

What is the d/(dt)((x)(2t+2t^3)) ?
The d/(dt)((x)(2t+2t^3)) is (dx)/(dt)(2t+2t^3)+(2+6t^2)x
What is the first d/(dt)((x)(2t+2t^3)) ?
The first d/(dt)((x)(2t+2t^3)) is (dx)/(dt)(2t+2t^3)+(2+6t^2)x