What is (\partial)/(\partial y)(e^x(1-cos(y))) ?

The answer to (\partial)/(\partial y)(e^x(1-cos(y))) is e^xsin(y)

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(\partial)/(\partial y)(e^x(1-cos(y)))

\frac{\partial}{\partial y} (e^{x} (1 - cos (y)))

e^{x} sin (y)

Solution steps

\frac{\partial}{\partial y} (e^{x} (1 - cos (y)))

Treat

x

as a constant

Take the constant out:

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

= e^{x} \frac{\partial}{\partial y} (1 - cos (y))

Apply the Sum/Difference Rule:

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

= e^{x} (\frac{\partial}{\partial y} (1) - \frac{\partial}{\partial y} (cos (y)))

\frac{\partial}{\partial y} (1) = 0

\frac{\partial}{\partial y} (cos (y)) = - sin (y)

= e^{x} (0 - (- sin (y)))

Simplify

= e^{x} sin (y)

\frac{4}{s - 2}

y^{^{'}} = \frac{( x ^{2} + 3 y ^{2} )}{2 x y}

x \to - 2 lim (2 x + 3)

(2 t^{2} - 1)^{3}

What is (\partial)/(\partial y)(e^x(1-cos(y))) ?
The answer to (\partial)/(\partial y)(e^x(1-cos(y))) is e^xsin(y)