What is the derivative of f(x)=(x+2)^x ?

The derivative of f(x)=(x+2)^x is (ln(x+2)+x/(x+2))(x+2)^x

What is the first derivative of f(x)=(x+2)^x ?

The first derivative of f(x)=(x+2)^x is (ln(x+2)+x/(x+2))(x+2)^x

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derivative of

f (x) = (x + 2)^{x}

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

What is the derivative of f(x)=(x+2)^x ?
The derivative of f(x)=(x+2)^x is (ln(x+2)+x/(x+2))(x+2)^x
What is the first derivative of f(x)=(x+2)^x ?
The first derivative of f(x)=(x+2)^x is (ln(x+2)+x/(x+2))(x+2)^x