What is the derivative of h(w)=(w^2-1)/(w^2+1) ?

The derivative of h(w)=(w^2-1)/(w^2+1) is (4w)/((w^2+1)^2)

What is the first derivative of h(w)=(w^2-1)/(w^2+1) ?

The first derivative of h(w)=(w^2-1)/(w^2+1) is (4w)/((w^2+1)^2)

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derivative of

h (w) = \frac{w ^{2} - 1}{w ^{2} + 1}

\frac{4 w}{( w ^{2} + 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Expand

2 w (w^{2} + 1) - 2 w (w^{2} - 1) : 4 w

= \frac{4 w}{( w ^{2} + 1 ) ^{2}}

\frac{d}{d x} (\frac{x ^{3}}{12})

\frac{1}{2} (9 t^{2} + t)^{- 3}

\int_{0}^{1} x^{2} + x d x

y^{^{''}} + y = 0, y (0) = 0

(5, 2), (- 2, - 2)

What is the derivative of h(w)=(w^2-1)/(w^2+1) ?
The derivative of h(w)=(w^2-1)/(w^2+1) is (4w)/((w^2+1)^2)
What is the first derivative of h(w)=(w^2-1)/(w^2+1) ?
The first derivative of h(w)=(w^2-1)/(w^2+1) is (4w)/((w^2+1)^2)