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Popular >

derivative of (x+3^x)

Solution

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

Solution

(ln (x + 3) + \frac{x}{x + 3}) (x + 3)^{x}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

= (ln (x + 3) + \frac{x}{x + 3}) (x + 3)^{x}

Popular Examples

derivative of x^{5e^x}

\frac{d}{d x} (x^{5 e^{x}})

area ln(x/2-3),[7,9]area

ln (\frac{x}{2} - 3), [7, 9]

integral from 0 to 3 of integral from 0 to y of e^{-y^2}

\int_{0}^{3} \int_{0}^{y} e^{- y^{2}} d x d y

integral of x^2+3x+C

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

sum from n=0 to infinity of n(6/7)^n

n = 0 \sum \infty n (\frac{6}{7})^{n}

Frequently Asked Questions (FAQ)

What is the derivative of (x+3^x) ?
The derivative of (x+3^x) is (ln(x+3)+x/(x+3))(x+3)^x
What is the first derivative of (x+3^x) ?
The first derivative of (x+3^x) is (ln(x+3)+x/(x+3))(x+3)^x