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Popular >

derivative of sqrt(y-x^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of (48x)/(4x^2+e)

\int \frac{48 x}{4 x ^{2} + e} d x

integral from-1 to 1 of x/(x^2+1)

\int_{- 1}^{1} \frac{x}{x ^{2} + 1} d x

integral of 5x^{2/3}

\int 5 x^{\frac{2}{3}} d x

tangent of y=6x^2-x^3,(1,5)tangent of

y = 6 x^{2} - x^{3}, (1, 5)

sum from n=0 to infinity of 1/(1!)

n = 0 \sum \infty \frac{1}{1 !}

Frequently Asked Questions (FAQ)

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