What is the first d/(du)(cos(u)) ?

The first d/(du)(cos(u)) is -sin(u)

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d/(du)(cos(u))

\frac{d}{d u} (cos (u))

- sin (u)

Solution steps

\frac{d}{d u} (cos (u))

Apply the common derivative:

\frac{d}{d u} (cos (u)) = - sin (u)

= - sin (u)

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 4, y^{^{'}} (0) = - 3

\frac{d}{d x} (\frac{x ^{2} - 3 x + 1}{x ^{2}})

x \to - 1 lim (8 x^{4} - 3 x^{3} + 7 x)

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

\frac{\partial}{\partial x} (ln (x + y))