What is the derivative of h(w)=(5w^3-w)/w ?

The derivative of h(w)=(5w^3-w)/w is 10w

What is the first derivative of h(w)=(5w^3-w)/w ?

The first derivative of h(w)=(5w^3-w)/w is 10w

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derivative of

h (w) = \frac{5 w ^{3} - w}{w}

10 w

Solution steps

\frac{d}{d w} (\frac{5 w ^{3} - w}{w})

Simplify

\frac{5 w ^{3} - w}{w} : 5 w^{2} - 1

= \frac{d}{d w} (5 w^{2} - 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d w} (5 w^{2}) - \frac{d}{d w} (1)

\frac{d}{d w} (5 w^{2}) = 10 w

\frac{d}{d w} (1) = 0

= 10 w - 0

Simplify

= 10 w

What is the derivative of h(w)=(5w^3-w)/w ?
The derivative of h(w)=(5w^3-w)/w is 10w
What is the first derivative of h(w)=(5w^3-w)/w ?
The first derivative of h(w)=(5w^3-w)/w is 10w