What is the d/(dt)((w)(t^2w^2)) ?

The d/(dt)((w)(t^2w^2)) is 2w^3t

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

The first d/(dt)((w)(t^2w^2)) is 2w^3t

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

2 w^{3} t

Solution steps

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

Simplify

(w) (t^{2} w^{2}) : w^{3} t^{2}

= \frac{d}{d t} (w^{3} t^{2})

Treat

w

as a constant

Take the constant out:

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

= w^{3} \frac{d}{d t} (t^{2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= w^{3} \cdot 2 t^{2 - 1}

Simplify

= 2 w^{3} t

(2 x^{3}) (8 x^{4})

e^{- l n^{2} (x)}

0.02 \cdot 1 0^{- 2}

4.5 \cdot 1 0^{- 1}

6 x (2 x^{4})