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Popular >

derivative of 3^{2x-1}

Solution

\frac{d}{d x} (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}

Popular Examples

integral of 1/((x^2-25)^2)

\int \frac{1}{( x ^{2} - 25 ) ^{2}} d x

tangent of f(x)=x^2+5,\at x=5 tangent of

f (x) = x^{2} + 5, at x = 5

limit as x approaches 3 of sqrt(2)

x \to 3 lim (2)

derivative of pi

\frac{d}{d x} (π)

sum from n=1 to infinity of n^{-1/9}

n = 1 \sum \infty n^{- \frac{1}{9}}

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}