What is the d/(dt)((θ)(θ^2-t^2)^2) ?

The d/(dt)((θ)(θ^2-t^2)^2) is -4θt(θ^2-t^2)

What is the first d/(dt)((θ)(θ^2-t^2)^2) ?

The first d/(dt)((θ)(θ^2-t^2)^2) is -4θt(θ^2-t^2)

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\frac{d}{d t} ((θ) (θ^{2} - t^{2})^{2})

- 4 θt (θ^{2} - t^{2})

Solution steps

\frac{d}{d t} ((θ) (θ^{2} - t^{2})^{2})

Treat

θ

as a constant

Take the constant out:

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

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

Apply the chain rule:

2 (θ^{2} - t^{2}) \frac{d}{d t} (θ^{2} - t^{2})

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

\frac{d}{d t} (θ^{2} - t^{2}) = - 2 t

= θ \cdot 2 (θ^{2} - t^{2}) (- 2 t)

Simplify

= - 4 θt (θ^{2} - t^{2})

\frac{\partial}{\partial x} ((z) (t x^{2} + yz - 2))

24 (1 - e^{- \frac{t}{2}})

x + 1 \cdot (x + 1)^{2}

(- cos (x) + \frac{cos ^{3} ( x )}{3})^{2}

\frac{sec ^{2} ( \frac{π}{4} )}{2 tan ( \frac{π}{4} )}

What is the d/(dt)((θ)(θ^2-t^2)^2) ?
The d/(dt)((θ)(θ^2-t^2)^2) is -4θt(θ^2-t^2)
What is the first d/(dt)((θ)(θ^2-t^2)^2) ?
The first d/(dt)((θ)(θ^2-t^2)^2) is -4θt(θ^2-t^2)