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Popular >

derivative of sqrt(x^2+2x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of y=((x^2+1)/(x^2-1))^6 derivative of

y = (\frac{x ^{2} + 1}{x ^{2} - 1})^{6}

derivative of cos(3xcos(2x))

\frac{d}{d x} (cos (3 x) cos (2 x))

tangent of f(x)=sqrt(7-6x),\at x=-1 tangent of

f (x) = 7 - 6 x, at x = - 1

derivative of ln(tan(x/2+pi/4))

\frac{d}{d x} (ln (tan (\frac{x}{2} + \frac{π}{4})))

integral of 9e^{3t}

\int 9 e^{3 t} d t

Frequently Asked Questions (FAQ)

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