What is the first d/(dz)(sh(z+i)) ?

The first d/(dz)(sh(z+i)) is sh

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d/(dz)(sh(z+i))

\frac{d}{d z} (s h (z + i))

s h

Solution steps

\frac{d}{d z} (s h (z + i))

Simplify

s h (z + i) : s h z + i s h

= \frac{d}{d z} (s h z + i s h)

Treat

s, h

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d}{d z} (s h z) + \frac{d}{d z} (i s h)

\frac{d}{d z} (s h z) = s h

\frac{d}{d z} (i s h) = 0

= s h + 0

Simplify

= s h

e - 2 t (sin (2 t) + 1)

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\frac{17 x - 16}{( x - 1 ) ^{2}}

(t^{2} + 2 t) \cdot cos (4 t)

\frac{( 0.77 W + ( 0.61 W + 612 ) ^{2.04} )}{W}