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Popular Calculus >

derivative of 17^{x-1}

Solution

derivative of

1 7^{x - 1}

Solution

ln (17) \cdot 1 7^{x - 1}

Solution steps

\frac{d}{d x} (1 7^{x - 1})

Apply exponent rule:

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

1 7^{x - 1} = e^{(x - 1) l n (17)}

= \frac{d}{d x} (e^{(x - 1) l n (17)})

Apply the chain rule:

e^{(x - 1) l n (17)} \frac{d}{d x} ((x - 1) ln (17))

= e^{(x - 1) l n (17)} \frac{d}{d x} ((x - 1) ln (17))

\frac{d}{d x} ((x - 1) ln (17)) = ln (17)

= e^{(x - 1) l n (17)} ln (17)

e^{(x - 1) l n (17)} = 1 7^{x - 1}

= ln (17) \cdot 1 7^{x - 1}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 17^{x-1} ?
The derivative of 17^{x-1} is ln(17)*17^{x-1}
What is the first derivative of 17^{x-1} ?
The first derivative of 17^{x-1} is ln(17)*17^{x-1}