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Popular >

derivative of sqrt(y^2-x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

simplify e^{ln(sin(x^2))}sqrt(2x+1)simplify

e^{l n (s i n (x^{2}))} 2 x + 1

limit as x approaches 0 of (ln(x+1))/x

x \to 0 lim (\frac{ln ( x + 1 )}{x})

integral of cos^2(10x)

\int cos^{2} (10 x) d x

derivative of (x^4+2^{cos(x)})

\frac{d}{d x} ((x^{4} + 2)^{c o s (x)})

limit as x approaches-3 of x^3

x \to - 3 lim (x^{3})

Frequently Asked Questions (FAQ)

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