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

The derivative of 1/(sqrt(1-x^2-y)) is -(-2x-\frac{dy)/(dx)}{2(1-x^2-y)^{3/2}}

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

The first derivative of 1/(sqrt(1-x^2-y)) is -(-2x-\frac{dy)/(dx)}{2(1-x^2-y)^{3/2}}

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

- \frac{- 2 x - \frac{d y}{d x}}{2 ( 1 - x ^{2} - y ) ^{\frac{3}{2}}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{1}{2 ( 1 - x ^{2} - y ) ^{\frac{3}{2}}} \frac{d}{d x} (1 - x^{2} - y)

= - \frac{1}{2 ( 1 - x ^{2} - y ) ^{\frac{3}{2}}} \frac{d}{d x} (1 - x^{2} - y)

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

= - \frac{1}{2 ( 1 - x ^{2} - y ) ^{\frac{3}{2}}} (- 2 x - \frac{d y}{d x})

Simplify

- \frac{1}{2 ( 1 - x ^{2} - y ) ^{\frac{3}{2}}} (- 2 x - \frac{d y}{d x}) : - \frac{- 2 x - \frac{d y}{d x}}{2 ( 1 - x ^{2} - y ) ^{\frac{3}{2}}}

= - \frac{- 2 x - \frac{d y}{d x}}{2 ( 1 - x ^{2} - y ) ^{\frac{3}{2}}}

\int \frac{e ^{\frac{4}{t}}}{t ^{2}} d t

\frac{d}{d x} (\frac{8 - x e ^{x}}{x + e ^{x}})

\int + \frac{1}{- x ^{2} + 8 x - 15} d x

(\frac{x ^{2}}{e ^{2 x}})^{6}

- 7 x + \frac{3}{x ^{6}}

What is the derivative of 1/(sqrt(1-x^2-y)) ?
The derivative of 1/(sqrt(1-x^2-y)) is -(-2x-\frac{dy)/(dx)}{2(1-x^2-y)^{3/2}}
What is the first derivative of 1/(sqrt(1-x^2-y)) ?
The first derivative of 1/(sqrt(1-x^2-y)) is -(-2x-\frac{dy)/(dx)}{2(1-x^2-y)^{3/2}}