What is the derivative of arctan(x/(4-sqrt(16-x^2))) ?

The derivative of arctan(x/(4-sqrt(16-x^2))) is -1/(2sqrt(-x^2+16))

What is the first derivative of arctan(x/(4-sqrt(16-x^2))) ?

The first derivative of arctan(x/(4-sqrt(16-x^2))) is -1/(2sqrt(-x^2+16))

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\frac{d}{d x} (arctan (\frac{x}{4 - 16 - x ^{2}}))

- \frac{1}{2 - x ^{2} + 16}

Solution steps

\frac{d}{d x} (arctan (\frac{x}{4 - 16 - x ^{2}}))

Apply the chain rule:

\frac{1}{( \frac{x}{4 - 16 - x ^{2}} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{4 - 16 - x ^{2}})

= \frac{1}{( \frac{x}{4 - 16 - x ^{2}} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{4 - 16 - x ^{2}})

\frac{d}{d x} (\frac{x}{4 - 16 - x ^{2}}) = \frac{4}{( - x ^{2} + 16 - 4 ) - x ^{2} + 16}

= \frac{1}{( \frac{x}{4 - 16 - x ^{2}} ) ^{2} + 1} \cdot \frac{4}{( - x ^{2} + 16 - 4 ) - x ^{2} + 16}

Simplify

\frac{1}{( \frac{x}{4 - 16 - x ^{2}} ) ^{2} + 1} \cdot \frac{4}{( - x ^{2} + 16 - 4 ) - x ^{2} + 16} : - \frac{1}{2 - x ^{2} + 16}

= - \frac{1}{2 - x ^{2} + 16}

x \to 1 lim (\frac{2 x}{6 x - 10})

\frac{d}{d x} (60)

x x (9.27)

\int \frac{2 x ^{2} + 3}{x ( x - 1 ) ^{2}} d x

\int \frac{( 3 x + 4 )}{x + 3} d x

What is the derivative of arctan(x/(4-sqrt(16-x^2))) ?
The derivative of arctan(x/(4-sqrt(16-x^2))) is -1/(2sqrt(-x^2+16))
What is the first derivative of arctan(x/(4-sqrt(16-x^2))) ?
The first derivative of arctan(x/(4-sqrt(16-x^2))) is -1/(2sqrt(-x^2+16))