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Popular >

derivative of arctan(sqrt(7x^2-1))

Solution

\frac{d}{d x} (arctan (7 x^{2} - 1))

Solution

\frac{1}{x 7 x ^{2} - 1}

Solution steps

\frac{d}{d x} (arctan (7 x^{2} - 1))

Apply the chain rule:

\frac{1}{( 7 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (7 x^{2} - 1)

= \frac{1}{( 7 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (7 x^{2} - 1)

\frac{d}{d x} (7 x^{2} - 1) = \frac{7 x}{7 x ^{2} - 1}

= \frac{1}{( 7 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{7 x}{7 x ^{2} - 1}

Simplify

\frac{1}{( 7 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{7 x}{7 x ^{2} - 1} : \frac{1}{x 7 x ^{2} - 1}

= \frac{1}{x 7 x ^{2} - 1}

Popular Examples

derivative of (8x^2+2x+4/(sqrt(x)))

\frac{d}{d x} (\frac{8 x ^{2} + 2 x + 4}{x})

integral of (4x-1)/((x+9)(x+2))

\int \frac{4 x - 1}{( x + 9 ) ( x + 2 )} d x

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\int_{3}^{4} - x^{2} + 7 x - 12 d x

integral of 9x^2ln(x)

\int 9 x^{2} ln (x) d x

limit as x approaches 6+of ln(x^2-36)

x \to 6 + lim (ln (x^{2} - 36))

Frequently Asked Questions (FAQ)

What is the derivative of arctan(sqrt(7x^2-1)) ?
The derivative of arctan(sqrt(7x^2-1)) is 1/(xsqrt(7x^2-1))
What is the first derivative of arctan(sqrt(7x^2-1)) ?
The first derivative of arctan(sqrt(7x^2-1)) is 1/(xsqrt(7x^2-1))