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Popular >

derivative of 5^{2x+1}

Solution

\frac{d}{d x} (5^{2 x + 1})

Solution

2 ln (5) \cdot 5^{2 x + 1}

Solution steps

\frac{d}{d x} (5^{2 x + 1})

Apply exponent rule:

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

5^{2 x + 1} = e^{(2 x + 1) l n (5)}

= \frac{d}{d x} (e^{(2 x + 1) l n (5)})

Apply the chain rule:

e^{(2 x + 1) l n (5)} \frac{d}{d x} ((2 x + 1) ln (5))

= e^{(2 x + 1) l n (5)} \frac{d}{d x} ((2 x + 1) ln (5))

\frac{d}{d x} ((2 x + 1) ln (5)) = 2 ln (5)

= e^{(2 x + 1) l n (5)} \cdot 2 ln (5)

e^{(2 x + 1) l n (5)} = 5^{2 x + 1}

= 2 ln (5) \cdot 5^{2 x + 1}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 5^{2x+1} ?
The derivative of 5^{2x+1} is 2ln(5)*5^{2x+1}
What is the first derivative of 5^{2x+1} ?
The first derivative of 5^{2x+1} is 2ln(5)*5^{2x+1}