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Popular >

derivative of y=arctan((4x)/3)

Solution

derivative of

y = arctan (\frac{4 x}{3})

Solution

\frac{12}{16 x ^{2} + 9}

Solution steps

\frac{d}{d x} (arctan (\frac{4 x}{3}))

Apply the chain rule:

\frac{1}{( \frac{4 x}{3} ) ^{2} + 1} \frac{d}{d x} (\frac{4 x}{3})

= \frac{1}{( \frac{4 x}{3} ) ^{2} + 1} \frac{d}{d x} (\frac{4 x}{3})

\frac{d}{d x} (\frac{4 x}{3}) = \frac{4}{3}

= \frac{1}{( \frac{4 x}{3} ) ^{2} + 1} \cdot \frac{4}{3}

Simplify

\frac{1}{( \frac{4 x}{3} ) ^{2} + 1} \cdot \frac{4}{3} : \frac{12}{16 x ^{2} + 9}

= \frac{12}{16 x ^{2} + 9}

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\int \frac{1}{16 - x ^{2}} d x

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Frequently Asked Questions (FAQ)

What is the derivative of y=arctan((4x)/3) ?
The derivative of y=arctan((4x)/3) is (12)/(16x^2+9)
What is the first derivative of y=arctan((4x)/3) ?
The first derivative of y=arctan((4x)/3) is (12)/(16x^2+9)