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Popular >

derivative of sqrt(x^2+y)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

d/(dy)(t/(2y^4))

\frac{d}{d y} (\frac{t}{2 y ^{4}})

integral of 1/(sqrt(64x^2+1))

\int \frac{1}{64 x ^{2} + 1} d x

6x^2((dy)/(dx))=((dy)/(dx))+9xe^{-y}

6 x^{2} (\frac{d y}{d x}) = (\frac{d y}{d x}) + 9 x e^{- y}

integral of 8x^{-3}

\int 8 x^{- 3} d x

integral from 0 to 2 of e^{-x}

\int_{0}^{2} e^{- x} d x

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x^2+y) ?
The derivative of sqrt(x^2+y) is (2x+\frac{dy)/(dx)}{2sqrt(x^2+y)}
What is the first derivative of sqrt(x^2+y) ?
The first derivative of sqrt(x^2+y) is (2x+\frac{dy)/(dx)}{2sqrt(x^2+y)}