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

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

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

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

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

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

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

\frac{1}{4 - x}

4 x - 1

y^{^{'}} = \frac{( x - 8 )}{x}

\frac{\partial}{\partial x} (U (x) (1 + \frac{R ( x ) ^{3}}{x ^{3}}))

2 x + y^{2} = 48, x = y

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