What is the derivative of 1/2 (e^x-cos(x)) ?

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

What is the first derivative of 1/2 (e^x-cos(x)) ?

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

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

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

Solution steps

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

Take the constant out:

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

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

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

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

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

Simplify

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

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