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Popular >

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

Solution

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

Solution

\frac{e ^{x}}{2 3 e ^{x}}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 \frac{e ^{x}}{3}} \cdot \frac{1}{3} e^{x}

Simplify

\frac{1}{2 \frac{e ^{x}}{3}} \cdot \frac{1}{3} e^{x} : \frac{e ^{x}}{2 3 e ^{x}}

= \frac{e ^{x}}{2 3 e ^{x}}

Popular Examples

integral from 4y^2+4z^2 to 4 of x

\int_{4 y^{2} + 4 z^{2}}^{4} x d x

derivative of (x^2-1(x^3+3x))

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

(y^{2})^{^{'}}

derivative of f(x)=x^2-sqrt(x)+2 derivative of

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

(dy)/(dx)y=x^{-12}

\frac{d y}{d x} y = x^{- 12}

Frequently Asked Questions (FAQ)

What is the derivative of sqrt((e^x/3)) ?
The derivative of sqrt((e^x/3)) is (e^x)/(2sqrt(3)\sqrt{e^x)}
What is the first derivative of sqrt((e^x/3)) ?
The first derivative of sqrt((e^x/3)) is (e^x)/(2sqrt(3)\sqrt{e^x)}