What is the derivative of sqrt(x^2+(y-1^2)) ?

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

What is the first derivative of sqrt(x^2+(y-1^2)) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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