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Popular >

derivative of 3^{2x+1}

Solution

derivative of

3^{2 x + 1}

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

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x \to 3 - lim (x - 3)

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x \to 1 lim (\frac{x + 9}{x + 1})

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x \to - 2 lim (\frac{x ^{2} - 1}{x - 1})

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\int sin (x) (cos (x))^{4} d x

Frequently Asked Questions (FAQ)

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