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Popular >

derivative of 2^{x-1}

Solution

derivative of

2^{x - 1}

Solution

ln (2) \cdot 2^{x - 1}

Solution steps

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

Apply exponent rule:

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

2^{x - 1} = e^{(x - 1) l n (2)}

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

Apply the chain rule:

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

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

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

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

e^{(x - 1) l n (2)} = 2^{x - 1}

= ln (2) \cdot 2^{x - 1}

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Frequently Asked Questions (FAQ)

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