What is the derivative of 2^{x+3} ?

The derivative of 2^{x+3} is ln(2)*2^{x+3}

What is the first derivative of 2^{x+3} ?

The first derivative of 2^{x+3} is ln(2)*2^{x+3}

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derivative of

2^{x + 3}

ln (2) \cdot 2^{x + 3}

Solution steps

\frac{d}{d x} (2^{x + 3})

Apply exponent rule:

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

2^{x + 3} = e^{(x + 3) l n (2)}

= \frac{d}{d x} (e^{(x + 3) l n (2)})

Apply the chain rule:

e^{(x + 3) l n (2)} \frac{d}{d x} ((x + 3) ln (2))

= e^{(x + 3) l n (2)} \frac{d}{d x} ((x + 3) ln (2))

\frac{d}{d x} ((x + 3) ln (2)) = ln (2)

= e^{(x + 3) l n (2)} ln (2)

e^{(x + 3) l n (2)} = 2^{x + 3}

= ln (2) \cdot 2^{x + 3}

\int \frac{x ^{3}}{3 x ^{2} + 3} d x

Y^{3}

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

What is the derivative of 2^{x+3} ?
The derivative of 2^{x+3} is ln(2)*2^{x+3}
What is the first derivative of 2^{x+3} ?
The first derivative of 2^{x+3} is ln(2)*2^{x+3}