What is the d/(dt)(({z}(t))(t^3)) ?

The d/(dt)(({z}(t))(t^3)) is d/(dt)({z}(t))t^3+3t^2{z}(t)

What is the first d/(dt)(({z}(t))(t^3)) ?

The first d/(dt)(({z}(t))(t^3)) is d/(dt)({z}(t))t^3+3t^2{z}(t)

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\frac{d}{d t} ((z (t)) (t^{3}))

\frac{d}{d t} (z (t)) t^{3} + 3 t^{2} z (t)

Solution steps

\frac{d}{d t} ((z (t)) (t^{3}))

Apply the Product Rule:

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

f = z (t), g = t^{3}

= \frac{d}{d t} (z (t)) t^{3} + \frac{d}{d t} (t^{3}) z (t)

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

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

3 (ln (3))

(ln (x)) (2 x cos (x^{2}))

(3 N) cos (14 0^{\circ})

x^{2 + 3 x + 3}

\frac{d ^{2}}{d t ^{2}} ((y) (A y))

What is the d/(dt)(({z}(t))(t^3)) ?
The d/(dt)(({z}(t))(t^3)) is d/(dt)({z}(t))t^3+3t^2{z}(t)
What is the first d/(dt)(({z}(t))(t^3)) ?
The first d/(dt)(({z}(t))(t^3)) is d/(dt)({z}(t))t^3+3t^2{z}(t)