What is the d/(dt)((x(t,C))(1-1/(k*t*C))) ?

The d/(dt)((x(t,C))(1-1/(k*t*C))) is d/(dt)({x}(t,C))(1-1/(ktC))+1/(Ckt^2){x}(t,C)

What is the first d/(dt)((x(t,C))(1-1/(k*t*C))) ?

The first d/(dt)((x(t,C))(1-1/(k*t*C))) is d/(dt)({x}(t,C))(1-1/(ktC))+1/(Ckt^2){x}(t,C)

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\frac{d}{d t} ((x (t, C)) (1 - \frac{1}{k \cdot t \cdot C}))

\frac{d}{d t} (x (t, C)) (1 - \frac{1}{k tC}) + \frac{1}{C k t ^{2}} x (t, C)

Solution steps

\frac{d}{d t} ((x (t, C)) (1 - \frac{1}{k tC}))

Treat

k, C

as a constant

Apply the Product Rule:

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

f = x (t, C), g = 1 - \frac{1}{k tC}

= \frac{d}{d t} (x (t, C)) (1 - \frac{1}{k tC}) + \frac{d}{d t} (1 - \frac{1}{k tC}) x (t, C)

\frac{d}{d t} (1 - \frac{1}{k tC}) = \frac{1}{C k t ^{2}}

= \frac{d}{d t} (x (t, C)) (1 - \frac{1}{k tC}) + \frac{1}{C k t ^{2}} x (t, C)

\frac{( 4 y ^{2} + 84 ) + ( y ^{3} - 4 y )}{( y ^{2} - 4 ) ( y + 2 )}

(x - 23) (x + 23) (x^{2} + 25)

(s + 1)^{2}

\frac{( x ^{2} + 10 s + 21 )}{( 9 s ( s + 7 ) )}

(x 2 + y) (x 2 - y)

What is the d/(dt)((x(t,C))(1-1/(k*t*C))) ?
The d/(dt)((x(t,C))(1-1/(k*t*C))) is d/(dt)({x}(t,C))(1-1/(ktC))+1/(Ckt^2){x}(t,C)
What is the first d/(dt)((x(t,C))(1-1/(k*t*C))) ?
The first d/(dt)((x(t,C))(1-1/(k*t*C))) is d/(dt)({x}(t,C))(1-1/(ktC))+1/(Ckt^2){x}(t,C)