What is the derivative of 4v^4-(12v^3+9v) ?

The derivative of 4v^4-(12v^3+9v) is 16v^3-36v^2-9

What is the first derivative of 4v^4-(12v^3+9v) ?

The first derivative of 4v^4-(12v^3+9v) is 16v^3-36v^2-9

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derivative of

4 v^{4} - (12 v^{3} + 9 v)

16 v^{3} - 36 v^{2} - 9

Solution steps

\frac{d}{d v} (4 v^{4} - (12 v^{3} + 9 v))

Simplify

4 v^{4} - (12 v^{3} + 9 v) : 4 v^{4} - 12 v^{3} - 9 v

= \frac{d}{d v} (4 v^{4} - 12 v^{3} - 9 v)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d v} (4 v^{4}) - \frac{d}{d v} (12 v^{3}) - \frac{d}{d v} (9 v)

\frac{d}{d v} (4 v^{4}) = 16 v^{3}

\frac{d}{d v} (12 v^{3}) = 36 v^{2}

\frac{d}{d v} (9 v) = 9

= 16 v^{3} - 36 v^{2} - 9

What is the derivative of 4v^4-(12v^3+9v) ?
The derivative of 4v^4-(12v^3+9v) is 16v^3-36v^2-9
What is the first derivative of 4v^4-(12v^3+9v) ?
The first derivative of 4v^4-(12v^3+9v) is 16v^3-36v^2-9