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Popular >

derivative of y=sqrt(e^2+2x)

Solution

derivative of

y = e^{2} + 2 x

Solution

\frac{1}{e ^{2} + 2 x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{e ^{2} + 2 x}

Popular Examples

limit as x approaches 0 of (e^x-1)/(15x)

x \to 0 lim (\frac{e ^{x} - 1}{15 x})

derivative of (e^{ax}-e^{-ax}/(e^{ax)+e^{-ax}})

\frac{d}{d x} (\frac{e ^{a x} - e ^{- a x}}{e ^{a x} + e ^{- a x}})

integral of 2xe^2x

\int 2 x e^{2} x d x

limit as x approaches 1 of sqrt(5-x)

x \to 1 lim (5 - x)

integral from 6 to 8 of (100)/((x-6)^3)

\int_{6}^{8} \frac{100}{( x - 6 ) ^{3}} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=sqrt(e^2+2x) ?
The derivative of y=sqrt(e^2+2x) is 1/(sqrt(e^2+2x))
What is the first derivative of y=sqrt(e^2+2x) ?
The first derivative of y=sqrt(e^2+2x) is 1/(sqrt(e^2+2x))