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Popular >

derivative of ((2+e^x/3)^9)

Solution

\frac{d}{d x} ((\frac{2 + e ^{x}}{3})^{9})

Solution

\frac{e ^{x} ( e ^{x} + 2 ) ^{8}}{2187}

Solution steps

\frac{d}{d x} ((\frac{2 + e ^{x}}{3})^{9})

Apply the chain rule:

9 (\frac{2 + e ^{x}}{3})^{8} \frac{d}{d x} (\frac{2 + e ^{x}}{3})

= 9 (\frac{2 + e ^{x}}{3})^{8} \frac{d}{d x} (\frac{2 + e ^{x}}{3})

\frac{d}{d x} (\frac{2 + e ^{x}}{3}) = \frac{1}{3} e^{x}

= 9 (\frac{2 + e ^{x}}{3})^{8} \frac{1}{3} e^{x}

Simplify

9 (\frac{2 + e ^{x}}{3})^{8} \frac{1}{3} e^{x} : \frac{e ^{x} ( e ^{x} + 2 ) ^{8}}{2187}

= \frac{e ^{x} ( e ^{x} + 2 ) ^{8}}{2187}

Graph

Popular Examples

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

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\int \frac{40}{1 - cos ( 8 x )} d x

limit as x approaches infinity of 67

x \to \infty lim (67)

integral from-2 to x of (x+2)/3

\int_{- 2}^{x} \frac{x + 2}{3} d x

derivative of (sqrt(3))/(x^9)derivative of

\frac{3}{x ^{9}}

Frequently Asked Questions (FAQ)

What is the derivative of ((2+e^x/3)^9) ?
The derivative of ((2+e^x/3)^9) is (e^x(e^x+2)^8)/(2187)
What is the first derivative of ((2+e^x/3)^9) ?
The first derivative of ((2+e^x/3)^9) is (e^x(e^x+2)^8)/(2187)