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Popular >

derivative of 2^{x+2}

Solution

derivative of

2^{x + 2}

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

Graph

Popular Examples

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\int \frac{1}{4 x + 8} d x

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\int \frac{2 x ln ( x )}{- x ^{4}} d x

(\partial)/(\partial x)(k(1+ae^{-b(x,w,t)x})(1+cos(wt)))

\frac{\partial}{\partial x} (k (1 + a e^{- b (x, w, t) x}) (1 + cos (wt)))

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\frac{d}{d x} ((7 x + 4)^{2})

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\int \frac{7}{x 4 - 49 ln ^{2} ( x )} d x

Frequently Asked Questions (FAQ)

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