What is the derivative of-2t(6t^6-1)^6 ?

The derivative of-2t(6t^6-1)^6 is -2((6t^6-1)^6+216t^6(6t^6-1)^5)

What is the first derivative of-2t(6t^6-1)^6 ?

The first derivative of-2t(6t^6-1)^6 is -2((6t^6-1)^6+216t^6(6t^6-1)^5)

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derivative of

- 2 t (6 t^{6} - 1)^{6}

- 2 ((6 t^{6} - 1)^{6} + 216 t^{6} (6 t^{6} - 1)^{5})

Solution steps

\frac{d}{d t} (- 2 t (6 t^{6} - 1)^{6})

Take the constant out:

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

= - 2 \frac{d}{d t} (t (6 t^{6} - 1)^{6})

Apply the Product Rule:

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

f = t, g = (6 t^{6} - 1)^{6}

= - 2 (\frac{d t}{d t} (6 t^{6} - 1)^{6} + \frac{d}{d t} ((6 t^{6} - 1)^{6}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} ((6 t^{6} - 1)^{6}) = 216 t^{5} (6 t^{6} - 1)^{5}

= - 2 (1 \cdot (6 t^{6} - 1)^{6} + 216 t^{5} (6 t^{6} - 1)^{5} t)

Simplify

- 2 (1 \cdot (6 t^{6} - 1)^{6} + 216 t^{5} (6 t^{6} - 1)^{5} t) : - 2 ((6 t^{6} - 1)^{6} + 216 t^{6} (6 t^{6} - 1)^{5})

= - 2 ((6 t^{6} - 1)^{6} + 216 t^{6} (6 t^{6} - 1)^{5})

What is the derivative of-2t(6t^6-1)^6 ?
The derivative of-2t(6t^6-1)^6 is -2((6t^6-1)^6+216t^6(6t^6-1)^5)
What is the first derivative of-2t(6t^6-1)^6 ?
The first derivative of-2t(6t^6-1)^6 is -2((6t^6-1)^6+216t^6(6t^6-1)^5)