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Popular >

derivative of 3^{x-1}

Solution

\frac{d}{d x} (3^{x - 1})

Solution

ln (3) \cdot 3^{x - 1}

Solution steps

\frac{d}{d x} (3^{x - 1})

Apply exponent rule:

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

3^{x - 1} = e^{(x - 1) l n (3)}

= \frac{d}{d x} (e^{(x - 1) l n (3)})

Apply the chain rule:

e^{(x - 1) l n (3)} \frac{d}{d x} ((x - 1) ln (3))

= e^{(x - 1) l n (3)} \frac{d}{d x} ((x - 1) ln (3))

\frac{d}{d x} ((x - 1) ln (3)) = ln (3)

= e^{(x - 1) l n (3)} ln (3)

e^{(x - 1) l n (3)} = 3^{x - 1}

= ln (3) \cdot 3^{x - 1}

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Frequently Asked Questions (FAQ)

What is the derivative of 3^{x-1} ?
The derivative of 3^{x-1} is ln(3)*3^{x-1}
What is the first derivative of 3^{x-1} ?
The first derivative of 3^{x-1} is ln(3)*3^{x-1}