What is the derivative of 6^{x+2} ?

The derivative of 6^{x+2} is ln(6)*6^{x+2}

What is the first derivative of 6^{x+2} ?

The first derivative of 6^{x+2} is ln(6)*6^{x+2}

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derivative of

6^{x + 2}

ln (6) \cdot 6^{x + 2}

Solution steps

\frac{d}{d x} (6^{x + 2})

Apply exponent rule:

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

6^{x + 2} = e^{(x + 2) l n (6)}

= \frac{d}{d x} (e^{(x + 2) l n (6)})

Apply the chain rule:

e^{(x + 2) l n (6)} \frac{d}{d x} ((x + 2) ln (6))

= e^{(x + 2) l n (6)} \frac{d}{d x} ((x + 2) ln (6))

\frac{d}{d x} ((x + 2) ln (6)) = ln (6)

= e^{(x + 2) l n (6)} ln (6)

e^{(x + 2) l n (6)} = 6^{x + 2}

= ln (6) \cdot 6^{x + 2}

What is the derivative of 6^{x+2} ?
The derivative of 6^{x+2} is ln(6)*6^{x+2}
What is the first derivative of 6^{x+2} ?
The first derivative of 6^{x+2} is ln(6)*6^{x+2}