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

The derivative of 1+csqrt(1-x^2) is -(cx)/(sqrt(-x^2+1))

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

The first derivative of 1+csqrt(1-x^2) is -(cx)/(sqrt(-x^2+1))

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (1) = 0

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

= 0 - \frac{c x}{1 - x ^{2}}

Simplify

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

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