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

The d/(dt)((x)(kx(t)^2)) is k(2t{x}(t)^2+2{x}(t) d/(dt)({x}(t))t^2)

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

The first d/(dt)((x)(kx(t)^2)) is k(2t{x}(t)^2+2{x}(t) d/(dt)({x}(t))t^2)

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 (t)) (k x (t) (t)^{2}))

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

Solution steps

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

Simplify

(x (t)) (k x (t) (t)^{2}) : k t^{2} x (t)^{2}

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = t^{2}, g = x (t)^{2}

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

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

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

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

3 p r - 2 q r - 12 p s + 8 q s

f (x) = 191.7 x^{432}

F e (N O^{3}) 3

9000 (1.00048)^{35}

\frac{d}{d w} ((z) (e^{z w}))

What is the d/(dt)((x)(kx(t)^2)) ?
The d/(dt)((x)(kx(t)^2)) is k(2t{x}(t)^2+2{x}(t) d/(dt)({x}(t))t^2)
What is the first d/(dt)((x)(kx(t)^2)) ?
The first d/(dt)((x)(kx(t)^2)) is k(2t{x}(t)^2+2{x}(t) d/(dt)({x}(t))t^2)