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Popular >

derivative of arctan((5x/4))

Solution

\frac{d}{d x} (arctan (\frac{5 x}{4}))

Solution

\frac{20}{25 x ^{2} + 16}

Solution steps

\frac{d}{d x} (arctan (\frac{5 x}{4}))

Apply the chain rule:

\frac{1}{( \frac{5 x}{4} ) ^{2} + 1} \frac{d}{d x} (\frac{5 x}{4})

= \frac{1}{( \frac{5 x}{4} ) ^{2} + 1} \frac{d}{d x} (\frac{5 x}{4})

\frac{d}{d x} (\frac{5 x}{4}) = \frac{5}{4}

= \frac{1}{( \frac{5 x}{4} ) ^{2} + 1} \cdot \frac{5}{4}

Simplify

\frac{1}{( \frac{5 x}{4} ) ^{2} + 1} \cdot \frac{5}{4} : \frac{20}{25 x ^{2} + 16}

= \frac{20}{25 x ^{2} + 16}

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Frequently Asked Questions (FAQ)

What is the derivative of arctan((5x/4)) ?
The derivative of arctan((5x/4)) is (20)/(25x^2+16)
What is the first derivative of arctan((5x/4)) ?
The first derivative of arctan((5x/4)) is (20)/(25x^2+16)