What is (\partial)/(\partial x)(sqrt(x^2+y^2-1)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+y^2-1)) is x/(sqrt(x^2+y^2-1))

(\partial)/(\partial x)(sqrt(x^2+y^2-1))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 x ^{2} + y ^{2} - 1} \cdot 2 x

Simplify

\frac{1}{2 x ^{2} + y ^{2} - 1} \cdot 2 x : \frac{x}{x ^{2} + y ^{2} - 1}

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

d er i v a t i v e f (x) = \frac{x ^{3}}{( x ^{2} + 4 ) ^{2}}

y^{^{'}} - \frac{3 y}{x} = x

d er i v a t i v e sin (x^{2}) + \frac{( 1 - x )}{1 + x}

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

k = 0 \sum \infty 5 x^{k}

What is (\partial)/(\partial x)(sqrt(x^2+y^2-1)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+y^2-1)) is x/(sqrt(x^2+y^2-1))