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Popular >

derivative of 2^{2x+1}

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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