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Popular >

derivative of 2^{x+1}

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

Graph

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\int e^{x} e^{2 x} + 4 d x

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(dy)/(dx)=sin(3y)ln(x)

\frac{d y}{d x} = sin (3 y) ln (x)

Frequently Asked Questions (FAQ)

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