What is the first d/(dz)(cos(z)) ?

The first d/(dz)(cos(z)) is -sin(z)

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d/(dz)(cos(z))

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

- sin (z)

Solution steps

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

Apply the common derivative:

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

= - sin (z)

x \to 0 lim (π)

d er i v a t i v e y = ln (\frac{7 + e ^{x}}{7 - e ^{x}})

y^{^{'}} = \frac{( 3 x ^{7} e ^{\frac{y}{x}} + x ^{5} y ^{2} )}{x ^{6} y}

x \to 0 lim (\frac{1 - cos ( 7 x )}{4 x ^{2}})

\int \frac{3}{2} x d x