What is the derivative of 2^{x/2} ?

The derivative of 2^{x/2} is 1/2 ln(2)e^{(ln(2)x)/2}

What is the first derivative of 2^{x/2} ?

The first derivative of 2^{x/2} is 1/2 ln(2)e^{(ln(2)x)/2}

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\frac{d}{d x} (2^{\frac{x}{2}})

\frac{1}{2} ln (2) e^{\frac{l n ( 2 ) x}{2}}

Solution steps

\frac{d}{d x} (2^{\frac{x}{2}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{\frac{x}{2}} = e^{\frac{x}{2} l n (2)}

= \frac{d}{d x} (e^{\frac{x}{2} l n (2)})

Apply the chain rule:

e^{\frac{x}{2} l n (2)} \frac{d}{d x} (\frac{x}{2} ln (2))

= e^{\frac{x}{2} l n (2)} \frac{d}{d x} (\frac{x}{2} ln (2))

\frac{d}{d x} (\frac{x}{2} ln (2)) = \frac{1}{2} ln (2)

= e^{\frac{x}{2} l n (2)} \frac{1}{2} ln (2)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1}{2} ln (2) e^{\frac{l n ( 2 ) x}{2}}

What is the derivative of 2^{x/2} ?
The derivative of 2^{x/2} is 1/2 ln(2)e^{(ln(2)x)/2}
What is the first derivative of 2^{x/2} ?
The first derivative of 2^{x/2} is 1/2 ln(2)e^{(ln(2)x)/2}