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Popular >

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

Solution

derivative of

y = e^{2 x} + x

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of f(x)=(4x)/(x+1)derivative of

f (x) = \frac{4 x}{x + 1}

integral of (x^5)/((8-x^6)^2)

\int \frac{x ^{5}}{( 8 - x ^{6} ) ^{2}} d x

integral of 2/(5x-8)

\int \frac{2}{5 x - 8} d x

integral of ((x^3-4x-10))/((x^2-x-6))

\int \frac{( x ^{3} - 4 x - 10 )}{( x ^{2} - x - 6 )} d x

integral of 5/((t^2+1)^{3/2)}

\int \frac{5}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

Frequently Asked Questions (FAQ)

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