What is (\partial)/(\partial t)((x)(2t^3-6t^2)) ?

The answer to (\partial)/(\partial t)((x)(2t^3-6t^2)) is x(6t^2-12t)

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(\partial)/(\partial t)((x)(2t^3-6t^2))

\frac{\partial}{\partial t} ((x) (2 t^{3} - 6 t^{2}))

x (6 t^{2} - 12 t)

Solution steps

\frac{\partial}{\partial t} ((x) (2 t^{3} - 6 t^{2}))

Treat

x

as a constant

Take the constant out:

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

= x \frac{\partial}{\partial t} (2 t^{3} - 6 t^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= x (\frac{\partial}{\partial t} (2 t^{3}) - \frac{\partial}{\partial t} (6 t^{2}))

\frac{\partial}{\partial t} (2 t^{3}) = 6 t^{2}

\frac{\partial}{\partial t} (6 t^{2}) = 12 t

= x (6 t^{2} - 12 t)

\frac{1}{3 ( x - 1 )}

\frac{x ^{3} - 6 x ^{2} + 4 x + 8}{( x - 3 ) ^{4}}

(1 + 2 sin (2 t)) \cdot (2 cos (t))

\frac{( 6 x ^{2} - 16 )}{( x + 1 ) ( 2 x - 3 )}

A (- 8, - 3, 1) y B (- 4, 3, 0)

What is (\partial)/(\partial t)((x)(2t^3-6t^2)) ?
The answer to (\partial)/(\partial t)((x)(2t^3-6t^2)) is x(6t^2-12t)