What is the derivative of 2t(3t^2-7)^5 ?

The derivative of 2t(3t^2-7)^5 is 2((3t^2-7)^5+30t^2(3t^2-7)^4)

What is the first derivative of 2t(3t^2-7)^5 ?

The first derivative of 2t(3t^2-7)^5 is 2((3t^2-7)^5+30t^2(3t^2-7)^4)

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derivative of

2 t (3 t^{2} - 7)^{5}

2 ((3 t^{2} - 7)^{5} + 30 t^{2} (3 t^{2} - 7)^{4})

Solution steps

\frac{d}{d t} (2 t (3 t^{2} - 7)^{5})

Take the constant out:

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

= 2 \frac{d}{d t} (t (3 t^{2} - 7)^{5})

Apply the Product Rule:

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

f = t, g = (3 t^{2} - 7)^{5}

= 2 (\frac{d t}{d t} (3 t^{2} - 7)^{5} + \frac{d}{d t} ((3 t^{2} - 7)^{5}) t)

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

\frac{d}{d t} ((3 t^{2} - 7)^{5}) = 30 t (3 t^{2} - 7)^{4}

= 2 (1 \cdot (3 t^{2} - 7)^{5} + 30 t (3 t^{2} - 7)^{4} t)

Simplify

2 (1 \cdot (3 t^{2} - 7)^{5} + 30 t (3 t^{2} - 7)^{4} t) : 2 ((3 t^{2} - 7)^{5} + 30 t^{2} (3 t^{2} - 7)^{4})

= 2 ((3 t^{2} - 7)^{5} + 30 t^{2} (3 t^{2} - 7)^{4})

What is the derivative of 2t(3t^2-7)^5 ?
The derivative of 2t(3t^2-7)^5 is 2((3t^2-7)^5+30t^2(3t^2-7)^4)
What is the first derivative of 2t(3t^2-7)^5 ?
The first derivative of 2t(3t^2-7)^5 is 2((3t^2-7)^5+30t^2(3t^2-7)^4)