What is the derivative of arctan(sqrt(4x^2-1)) ?

The derivative of arctan(sqrt(4x^2-1)) is 1/(xsqrt(4x^2-1))

What is the first derivative of arctan(sqrt(4x^2-1)) ?

The first derivative of arctan(sqrt(4x^2-1)) is 1/(xsqrt(4x^2-1))

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

\frac{1}{x 4 x ^{2} - 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x 4 x ^{2} - 1}

\int sin^{3} (2 θ) cot (2 θ) d θ

f (x) = 2 x^{3} - x^{2} + 2, (1, 3)

x \to - 1 + lim (f (x))

\int 5 x cos (6 x) d x

What is the derivative of arctan(sqrt(4x^2-1)) ?
The derivative of arctan(sqrt(4x^2-1)) is 1/(xsqrt(4x^2-1))
What is the first derivative of arctan(sqrt(4x^2-1)) ?
The first derivative of arctan(sqrt(4x^2-1)) is 1/(xsqrt(4x^2-1))