What is the derivative of 5(3t+4)^2 ?

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

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

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

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derivative of

5 (3 t + 4)^{2}

30 (3 t + 4)

Solution steps

\frac{d}{d t} (5 (3 t + 4)^{2})

Take the constant out:

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

= 5 \frac{d}{d t} ((3 t + 4)^{2})

Apply the chain rule:

2 (3 t + 4) \frac{d}{d t} (3 t + 4)

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

\frac{d}{d t} (3 t + 4) = 3

= 5 \cdot 2 (3 t + 4) \cdot 3

Simplify

= 30 (3 t + 4)

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