What is the d/(dm)(1/2 mv^2) ?

The d/(dm)(1/2 mv^2) is (v^2)/2+mv(dv)/(dm)

What is the first d/(dm)(1/2 mv^2) ?

The first d/(dm)(1/2 mv^2) is (v^2)/2+mv(dv)/(dm)

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\frac{d}{d m} (\frac{1}{2} m v^{2})

\frac{v ^{2}}{2} + m v \frac{d v}{d m}

Solution steps

\frac{d}{d m} (\frac{1}{2} m v^{2})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d m} (m v^{2})

Apply the Product Rule:

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

f = m, g = v^{2}

= \frac{1}{2} (\frac{d m}{d m} v^{2} + \frac{d}{d m} (v^{2}) m)

\frac{d m}{d m} = 1

\frac{d}{d m} (v^{2}) = 2 v \frac{d v}{d m}

= \frac{1}{2} (1 \cdot v^{2} + 2 v \frac{d v}{d m} m)

Simplify

\frac{1}{2} (1 \cdot v^{2} + 2 v \frac{d v}{d m} m) : \frac{v ^{2}}{2} + m v \frac{d v}{d m}

= \frac{v ^{2}}{2} + m v \frac{d v}{d m}

(2 + 5)^{2}

m - (- 5) < 14

a^{0}

\frac{40 - 20 ( 1 )}{1 ^{2}} + \frac{1}{2}

2 ∣ x - 1 ∣ = 0

What is the d/(dm)(1/2 mv^2) ?
The d/(dm)(1/2 mv^2) is (v^2)/2+mv(dv)/(dm)
What is the first d/(dm)(1/2 mv^2) ?
The first d/(dm)(1/2 mv^2) is (v^2)/2+mv(dv)/(dm)