What is the d/(dt)(1/2 {g}(t)t^2) ?

The d/(dt)(1/2 {g}(t)t^2) is (t^2 d/(dt)({g}(t)))/2+t{g}(t)

What is the first d/(dt)(1/2 {g}(t)t^2) ?

The first d/(dt)(1/2 {g}(t)t^2) is (t^2 d/(dt)({g}(t)))/2+t{g}(t)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d t} (\frac{1}{2} g (t) t^{2})

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

Solution steps

\frac{d}{d t} (\frac{1}{2} g (t) t^{2})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d t} (g (t) t^{2})

Apply the Product Rule:

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

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

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

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

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

Simplify

\frac{1}{2} (\frac{d}{d t} (g (t)) t^{2} + 2 t g (t)) : \frac{t ^{2} \frac{d}{d t} ( g ( t ) )}{2} + t g (t)

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

x^{2} \frac{d y}{d x} y^{2} = 0

\frac{\partial}{\partial x} (A e^{- 1 k x})

\int 2 x ln (3 x) d x

n = 1 \sum \infty 2 π^{- n}

x \to \infty lim (\frac{3 ^{3 \cdot x}}{3 ^{x}})

What is the d/(dt)(1/2 {g}(t)t^2) ?
The d/(dt)(1/2 {g}(t)t^2) is (t^2 d/(dt)({g}(t)))/2+t{g}(t)
What is the first d/(dt)(1/2 {g}(t)t^2) ?
The first d/(dt)(1/2 {g}(t)t^2) is (t^2 d/(dt)({g}(t)))/2+t{g}(t)