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

The derivative of sqrt(2-((x+1)^2)/2) is -(x+1)/(sqrt(2)\sqrt{-x^2-2x+3)}

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

The first derivative of sqrt(2-((x+1)^2)/2) is -(x+1)/(sqrt(2)\sqrt{-x^2-2x+3)}

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derivative of

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

- \frac{x + 1}{2 - x ^{2} - 2 x + 3}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{x + 1}{2 - x ^{2} - 2 x + 3}

\int \frac{5 x}{1 - 25 x ^{4}} d x

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

\frac{d}{d x} (e^{6 x} + 3 (ln (2))^{2} e^{2 x} - e^{4 x} ln (8) - (ln (2))^{3})

3 x

f (x) = - 2 x^{4} + 8 x^{2}

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