What is the (a(t)sin^3(t))^' ?

The (a(t)sin^3(t))^' is a(sin^3(t)+3tsin^2(t)cos(t))

What is the first (a(t)sin^3(t))^' ?

The first (a(t)sin^3(t))^' is a(sin^3(t)+3tsin^2(t)cos(t))

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(a (t) sin^{3} (t))^{^{'}}

a (sin^{3} (t) + 3 t sin^{2} (t) cos (t))

Solution steps

(a (t) sin^{3} (t))^{'}

Take the constant out:

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

= a (t sin^{3} (t))^{^{'}}

Apply the Product Rule:

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

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

= a (t^{^{'}} sin^{3} (t) + (sin^{3} (t))^{^{'}} t)

t^{'} = 1

(sin^{3} (t))^{'} = 3 sin^{2} (t) cos (t)

= a (1 \cdot sin^{3} (t) + 3 sin^{2} (t) cos (t) t)

Simplify

= a (sin^{3} (t) + 3 t sin^{2} (t) cos (t))

y = sin (7 x)

y^{^{''}} + 4 y^{^{'}} + \frac{17}{4} y = 0

\frac{\partial}{\partial x} (1 - cos (x))

\int cos (\frac{π}{2}) d x

- 19.6 t^{2} + 9 t + 3

What is the (a(t)sin^3(t))^' ?
The (a(t)sin^3(t))^' is a(sin^3(t)+3tsin^2(t)cos(t))
What is the first (a(t)sin^3(t))^' ?
The first (a(t)sin^3(t))^' is a(sin^3(t)+3tsin^2(t)cos(t))