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Popular >

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

Solution

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

Solution

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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

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

integral of x^3e^{2x}

\int x^{3} e^{2 x} d x

sum from n=1 to infinity of (n^5)/(2^n)

n = 1 \sum \infty \frac{n ^{5}}{2 ^{n}}

laplacetransform F(x)=sin(2x)-2xcos(2x)laplace transform

F (x) = sin (2 x) - 2 x cos (2 x)

integral of 2ye^{xy}

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

Frequently Asked Questions (FAQ)

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