What is the d/(dt)((x)200(30-t^2)) ?

The d/(dt)((x)200(30-t^2)) is 200((dx)/(dt)(30-t^2)-2tx)

What is the first d/(dt)((x)200(30-t^2)) ?

The first d/(dt)((x)200(30-t^2)) is 200((dx)/(dt)(30-t^2)-2tx)

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\frac{d}{d t} ((x) 200 (30 - t^{2}))

200 (\frac{d x}{d t} (30 - t^{2}) - 2 t x)

Solution steps

\frac{d}{d t} ((x) \cdot 200 (30 - t^{2}))

Take the constant out:

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

= 200 \frac{d}{d t} (x (30 - t^{2}))

Apply the Product Rule:

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

f = x, g = 30 - t^{2}

= 200 (\frac{d x}{d t} (30 - t^{2}) + \frac{d}{d t} (30 - t^{2}) x)

\frac{d}{d t} (30 - t^{2}) = - 2 t

= 200 (\frac{d x}{d t} (30 - t^{2}) + (- 2 t) x)

Simplify

= 200 (\frac{d x}{d t} (30 - t^{2}) - 2 t x)

\frac{x y ( x ^{2} - y ^{2} )}{x ^{2} + y ^{2}}

(1 + 2)^{6}

(\frac{4}{3} - x)^{2}

(t - b) e^{a t}

(x - 1)^{2} (x^{2} - 2 x + 1)

What is the d/(dt)((x)200(30-t^2)) ?
The d/(dt)((x)200(30-t^2)) is 200((dx)/(dt)(30-t^2)-2tx)
What is the first d/(dt)((x)200(30-t^2)) ?
The first d/(dt)((x)200(30-t^2)) is 200((dx)/(dt)(30-t^2)-2tx)