What is (\partial)/(\partial x)(sqrt(x^2+x)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+x)) is (2x+1)/(2sqrt(x^2+x))

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(\partial)/(\partial x)(sqrt(x^2+x))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 7 cot^{3} (x) csc^{3} (x) d x

f (y) = e^{3 y}

n = 0 \sum \infty 1 (n + 1)

\frac{d}{d x} (2 x csc (x) sec (x))

(2, 3), (6, - 5)

What is (\partial)/(\partial x)(sqrt(x^2+x)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+x)) is (2x+1)/(2sqrt(x^2+x))