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Popular >

derivative of sqrt(x-\sqrt{y)}

Solution

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

Solution

\frac{2 y - \frac{d y}{d x}}{4 y x - y}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x - y} (1 - \frac{\frac{d y}{d x}}{2 y}) : \frac{2 y - \frac{d y}{d x}}{4 y x - y}

= \frac{2 y - \frac{d y}{d x}}{4 y x - y}

Popular Examples

laplacetransform 3cos(3t)laplace transform

3 cos (3 t)

y^{''}+8y^'+19y=0,y(0)=3,y^'(0)=-4

y^{^{''}} + 8 y^{^{'}} + 19 y = 0, y (0) = 3, y^{^{'}} (0) = - 4

y^{'''}-2y^{''}-12y^'+16y=0

y^{^{'''}} - 2 y^{^{''}} - 12 y^{^{'}} + 16 y = 0

limit as x approaches-3+of-2/(x^2-9)

x \to - 3 + lim (- \frac{2}{x ^{2} - 9})

inverse oflaplace 3/((2s^2+8s+10))inverse laplace

\frac{3}{( 2 s ^{2} + 8 s + 10 )}

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x-\sqrt{y)} ?
The derivative of sqrt(x-\sqrt{y)} is (2sqrt(y)-\frac{dy)/(dx)}{4sqrt(y)sqrt(x-\sqrt{y)}}
What is the first derivative of sqrt(x-\sqrt{y)} ?
The first derivative of sqrt(x-\sqrt{y)} is (2sqrt(y)-\frac{dy)/(dx)}{4sqrt(y)sqrt(x-\sqrt{y)}}