What is the derivative of-5t(2t^7-1)^5 ?

The derivative of-5t(2t^7-1)^5 is -5((2t^7-1)^5+70t^7(2t^7-1)^4)

What is the first derivative of-5t(2t^7-1)^5 ?

The first derivative of-5t(2t^7-1)^5 is -5((2t^7-1)^5+70t^7(2t^7-1)^4)

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derivative of

- 5 t (2 t^{7} - 1)^{5}

- 5 ((2 t^{7} - 1)^{5} + 70 t^{7} (2 t^{7} - 1)^{4})

Solution steps

\frac{d}{d t} (- 5 t (2 t^{7} - 1)^{5})

Take the constant out:

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

= - 5 \frac{d}{d t} (t (2 t^{7} - 1)^{5})

Apply the Product Rule:

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

f = t, g = (2 t^{7} - 1)^{5}

= - 5 (\frac{d t}{d t} (2 t^{7} - 1)^{5} + \frac{d}{d t} ((2 t^{7} - 1)^{5}) t)

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

\frac{d}{d t} ((2 t^{7} - 1)^{5}) = 70 t^{6} (2 t^{7} - 1)^{4}

= - 5 (1 \cdot (2 t^{7} - 1)^{5} + 70 t^{6} (2 t^{7} - 1)^{4} t)

Simplify

- 5 (1 \cdot (2 t^{7} - 1)^{5} + 70 t^{6} (2 t^{7} - 1)^{4} t) : - 5 ((2 t^{7} - 1)^{5} + 70 t^{7} (2 t^{7} - 1)^{4})

= - 5 ((2 t^{7} - 1)^{5} + 70 t^{7} (2 t^{7} - 1)^{4})

What is the derivative of-5t(2t^7-1)^5 ?
The derivative of-5t(2t^7-1)^5 is -5((2t^7-1)^5+70t^7(2t^7-1)^4)
What is the first derivative of-5t(2t^7-1)^5 ?
The first derivative of-5t(2t^7-1)^5 is -5((2t^7-1)^5+70t^7(2t^7-1)^4)