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Popular >

derivative of sqrt(x-y^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of x^{2/3}(x-2)

\frac{d}{d x} (x^{\frac{2}{3}} (x - 2))

y^'=(3x^2+y^2)/(xy)

y^{^{'}} = \frac{3 x ^{2} + y ^{2}}{x y}

derivative of ln(sec(2x)+tan(2x))derivative of

ln (sec (2 x) + tan (2 x))

slope ofintercept (-3,-9),(8,3)slope intercept

(- 3, - 9), (8, 3)

derivative of f(x)=3x^2e^x+e^x(x^3+9)derivative of

f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 9)

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x-y^2) ?
The derivative of sqrt(x-y^2) is (1-2y\frac{dy)/(dx)}{2sqrt(x-y^2)}
What is the first derivative of sqrt(x-y^2) ?
The first derivative of sqrt(x-y^2) is (1-2y\frac{dy)/(dx)}{2sqrt(x-y^2)}