What is (\partial)/(\partial x)((z)(x+sin(x+z))) ?

The answer to (\partial)/(\partial x)((z)(x+sin(x+z))) is z(1+cos(x+z))

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(\partial)/(\partial x)((z)(x+sin(x+z)))

\frac{\partial}{\partial x} ((z) (x + sin (x + z)))

z (1 + cos (x + z))

Solution steps

\frac{\partial}{\partial x} ((z) (x + sin (x + z)))

Treat

z

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial x} (x + sin (x + z))

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (sin (x + z)))

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (sin (x + z)) = cos (x + z)

= z (1 + cos (x + z))

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

\frac{1}{5 x} (5)

\frac{( ( s - 1 ) e ^{- 2 s} )}{s ^{2} + 8 s + 13}

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

\frac{3.2 k}{( s ^{2} + 8 s + 1 ) ( s ^{2} + s + 3 ) + 3.2 k}

What is (\partial)/(\partial x)((z)(x+sin(x+z))) ?
The answer to (\partial)/(\partial x)((z)(x+sin(x+z))) is z(1+cos(x+z))