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

The derivative of (x^2-y^2)^{1/2} is x/((x^2-y^2)^{1/2)}

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

The first derivative of (x^2-y^2)^{1/2} is x/((x^2-y^2)^{1/2)}

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derivative of

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

d er i v a t i v e \frac{( ( x ^{6} ) - 1 )}{( ( x ^{6} ) + 1 )}

d er i v a t i v e y = 3 cos (x) + 7 e x + ln (x^{2} + 1)

d er i v a t i v e f (x) = \frac{4 x - 1}{x}

d er i v a t i v e 2^{z}

d er i v a t i v e y = sin (x^{- 1})

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