What is the derivative of y=(e^x+sin(x))/2 ?

The derivative of y=(e^x+sin(x))/2 is 1/2 (e^x+cos(x))

What is the first derivative of y=(e^x+sin(x))/2 ?

The first derivative of y=(e^x+sin(x))/2 is 1/2 (e^x+cos(x))

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derivative of

y = \frac{e ^{x} + sin ( x )}{2}

\frac{1}{2} (e^{x} + cos (x))

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (sin (x)) = cos (x)

= \frac{1}{2} (e^{x} + cos (x))

What is the derivative of y=(e^x+sin(x))/2 ?
The derivative of y=(e^x+sin(x))/2 is 1/2 (e^x+cos(x))
What is the first derivative of y=(e^x+sin(x))/2 ?
The first derivative of y=(e^x+sin(x))/2 is 1/2 (e^x+cos(x))