What is the derivative of 0.49489nv^2+1500*n/v ?

The derivative of 0.49489nv^2+1500*n/v is 0.98978nv-(1500n)/(v^2)

What is the first derivative of 0.49489nv^2+1500*n/v ?

The first derivative of 0.49489nv^2+1500*n/v is 0.98978nv-(1500n)/(v^2)

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derivative of

0.49489 n v^{2} + 1500 \cdot \frac{n}{v}

0.98978 n v - \frac{1500 n}{v ^{2}}

Solution steps

\frac{d}{d v} (0.49489 n v^{2} + 1500 \cdot \frac{n}{v})

Simplify

0.49489 n v^{2} + 1500 \cdot \frac{n}{v} : 0.49489 n v^{2} + \frac{1500 n}{v}

= \frac{d}{d v} (0.49489 n v^{2} + \frac{1500 n}{v})

Apply the Sum/Difference Rule:

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

= \frac{d}{d v} (0.49489 n v^{2}) + \frac{d}{d v} (\frac{1500 n}{v})

\frac{d}{d v} (0.49489 n v^{2}) = 0.98978 n v

\frac{d}{d v} (\frac{1500 n}{v}) = - \frac{1500 n}{v ^{2}}

= 0.98978 n v - \frac{1500 n}{v ^{2}}

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What is the derivative of 0.49489nv^2+1500*n/v ?
The derivative of 0.49489nv^2+1500*n/v is 0.98978nv-(1500n)/(v^2)
What is the first derivative of 0.49489nv^2+1500*n/v ?
The first derivative of 0.49489nv^2+1500*n/v is 0.98978nv-(1500n)/(v^2)