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Popular >

derivative of 2^{3x-1}

Solution

\frac{d}{d x} (2^{3 x - 1})

Solution

3 ln (2) \cdot 2^{3 x - 1}

Solution steps

\frac{d}{d x} (2^{3 x - 1})

Apply exponent rule:

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

2^{3 x - 1} = e^{(3 x - 1) l n (2)}

= \frac{d}{d x} (e^{(3 x - 1) l n (2)})

Apply the chain rule:

e^{(3 x - 1) l n (2)} \frac{d}{d x} ((3 x - 1) ln (2))

= e^{(3 x - 1) l n (2)} \frac{d}{d x} ((3 x - 1) ln (2))

\frac{d}{d x} ((3 x - 1) ln (2)) = 3 ln (2)

= e^{(3 x - 1) l n (2)} \cdot 3 ln (2)

e^{(3 x - 1) l n (2)} = 2^{3 x - 1}

= 3 ln (2) \cdot 2^{3 x - 1}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 2^{3x-1} ?
The derivative of 2^{3x-1} is 3ln(2)*2^{3x-1}
What is the first derivative of 2^{3x-1} ?
The first derivative of 2^{3x-1} is 3ln(2)*2^{3x-1}