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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x^{2} - 1) = 4 x

= \frac{1}{2 ( 2 x ^{2} - 1 ) ^{\frac{1}{2}}} \cdot 4 x

Simplify

\frac{1}{2 ( 2 x ^{2} - 1 ) ^{\frac{1}{2}}} \cdot 4 x : \frac{2 x}{( 2 x ^{2} - 1 ) ^{\frac{1}{2}}}

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

y^{^{''}} + 8 y^{^{'}} + 65 y = 0, y (0) = 0, y^{^{'}} (0) = 0

x \to - 2 lim (x^{2} - 2 x^{2} + 2 x + 3)

\frac{d}{d x} (\frac{tan ( x ) - 1}{sec ( x )})

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

\int 7 cos^{3} (x) d x

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