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Popular >

derivative of (x+2^x)

Solution

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

Solution

(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}

Popular Examples

integral of ((2+e^x)^2)/(e^x)

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

derivative of y=xsqrt(36-x^2)derivative of

y = x 36 - x^{2}

x y^{^{'}} + 3 y = x^{4} - x

integral of (e^x)/((5-e^x)^2)

\int \frac{e ^{x}}{( 5 - e ^{x} ) ^{2}} d x

integral of sin(x)e^{-sx}

\int sin (x) e^{- s x} d x

Frequently Asked Questions (FAQ)

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