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Popular >

derivative of arctan(x/4)

Solution

derivative of

arctan (\frac{x}{4})

Solution

\frac{4}{x ^{2} + 16}

Solution steps

\frac{d}{d x} (arctan (\frac{x}{4}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{4}) = \frac{1}{4}

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

Simplify

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

= \frac{4}{x ^{2} + 16}

Popular Examples

integral of ((4-x)^2)/(sqrt(x))

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

derivative of (e^x)/(e^x+3)derivative of

\frac{e ^{x}}{e ^{x} + 3}

integral of (4x)/(sqrt(x^2+1))

\int \frac{4 x}{x ^{2} + 1} d x

integral of x^2*2^x

\int x^{2} \cdot 2^{x} d x

derivative of f(x)=sqrt(x)+x^{2/3}-3x derivative of

f (x) = x + x^{\frac{2}{3}} - 3 x

Frequently Asked Questions (FAQ)

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