What is the derivative of arctan(sqrt(5x^2-1)) ?

The derivative of arctan(sqrt(5x^2-1)) is 1/(xsqrt(5x^2-1))

What is the first derivative of arctan(sqrt(5x^2-1)) ?

The first derivative of arctan(sqrt(5x^2-1)) is 1/(xsqrt(5x^2-1))

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\frac{d}{d x} (arctan (5 x^{2} - 1))

\frac{1}{x 5 x ^{2} - 1}

Solution steps

\frac{d}{d x} (arctan (5 x^{2} - 1))

Apply the chain rule:

\frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (5 x^{2} - 1)

= \frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (5 x^{2} - 1)

\frac{d}{d x} (5 x^{2} - 1) = \frac{5 x}{5 x ^{2} - 1}

= \frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{5 x}{5 x ^{2} - 1}

Simplify

\frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{5 x}{5 x ^{2} - 1} : \frac{1}{x 5 x ^{2} - 1}

= \frac{1}{x 5 x ^{2} - 1}

\int x^{3} x^{2} + 9 d x

\frac{\partial}{\partial x} (sin (π (6 x - y)))

arctan (\frac{1 + t}{1 - t})

\frac{d}{d x} (- 2 (arctan (3 x) - arctan (2 x)) + x)

\int \frac{3}{60 - t} d t

What is the derivative of arctan(sqrt(5x^2-1)) ?
The derivative of arctan(sqrt(5x^2-1)) is 1/(xsqrt(5x^2-1))
What is the first derivative of arctan(sqrt(5x^2-1)) ?
The first derivative of arctan(sqrt(5x^2-1)) is 1/(xsqrt(5x^2-1))