What is the first derivative of 1+w^2 ?

The first derivative of 1+w^2 is 2w

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derivative of 1+w^2

derivative of

1 + w^{2}

2 w

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + 2 w

Simplify

= 2 w

2 (x sin (x) + cos (x))

\frac{1}{3 x ^{2} + 2}

\frac{( cos ( x ) - cos ^{3} ( x ) )}{x ^{2}}

\frac{6}{2 - 4 x}

\frac{- 1}{( x + 1 ) ^{2}}