What is the derivative of arctan(sqrt(6x^2-1)) ?

The derivative of arctan(sqrt(6x^2-1)) is 1/(xsqrt(6x^2-1))

What is the first derivative of arctan(sqrt(6x^2-1)) ?

The first derivative of arctan(sqrt(6x^2-1)) is 1/(xsqrt(6x^2-1))

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derivative of

arctan (6 x^{2} - 1)

\frac{1}{x 6 x ^{2} - 1}

Solution steps

\frac{d}{d x} (arctan (6 x^{2} - 1))

Apply the chain rule:

\frac{1}{( 6 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (6 x^{2} - 1)

= \frac{1}{( 6 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (6 x^{2} - 1)

\frac{d}{d x} (6 x^{2} - 1) = \frac{6 x}{6 x ^{2} - 1}

= \frac{1}{( 6 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{6 x}{6 x ^{2} - 1}

Simplify

\frac{1}{( 6 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{6 x}{6 x ^{2} - 1} : \frac{1}{x 6 x ^{2} - 1}

= \frac{1}{x 6 x ^{2} - 1}

\int 8 x \cdot csc^{2} (4 x) d x

\int 2^{5 x + 2} d x

2 x y^{^{'}} + y = 6 x, y (4) = 15

\int \frac{x ^{'}}{x ^{2}} d x

What is the derivative of arctan(sqrt(6x^2-1)) ?
The derivative of arctan(sqrt(6x^2-1)) is 1/(xsqrt(6x^2-1))
What is the first derivative of arctan(sqrt(6x^2-1)) ?
The first derivative of arctan(sqrt(6x^2-1)) is 1/(xsqrt(6x^2-1))