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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

Simplify

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

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

\frac{1}{s ( 5 s + 4 )}

lo g_{10} (27) (81)

(1 + δ) (1 + δ)

- 2 (6 m - 7) + 3 (m - 13)^{'}

\frac{d}{d t} ((w) ((w - 2) (w - 3)))

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