What is the derivative of 2t(3t^3-7)^4 ?

The derivative of 2t(3t^3-7)^4 is 2((3t^3-7)^4+36t^3(3t^3-7)^3)

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

The first derivative of 2t(3t^3-7)^4 is 2((3t^3-7)^4+36t^3(3t^3-7)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

2 t (3 t^{3} - 7)^{4}

2 ((3 t^{3} - 7)^{4} + 36 t^{3} (3 t^{3} - 7)^{3})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = t, g = (3 t^{3} - 7)^{4}

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

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

\frac{d}{d t} ((3 t^{3} - 7)^{4}) = 36 t^{2} (3 t^{3} - 7)^{3}

= 2 (1 \cdot (3 t^{3} - 7)^{4} + 36 t^{2} (3 t^{3} - 7)^{3} t)

Simplify

2 (1 \cdot (3 t^{3} - 7)^{4} + 36 t^{2} (3 t^{3} - 7)^{3} t) : 2 ((3 t^{3} - 7)^{4} + 36 t^{3} (3 t^{3} - 7)^{3})

= 2 ((3 t^{3} - 7)^{4} + 36 t^{3} (3 t^{3} - 7)^{3})

What is the derivative of 2t(3t^3-7)^4 ?
The derivative of 2t(3t^3-7)^4 is 2((3t^3-7)^4+36t^3(3t^3-7)^3)
What is the first derivative of 2t(3t^3-7)^4 ?
The first derivative of 2t(3t^3-7)^4 is 2((3t^3-7)^4+36t^3(3t^3-7)^3)