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Popular >

derivative of y=arctan(sqrt(2t))

Solution

derivative of

y = arctan (2 t)

Solution

\frac{1}{2 t ( 2 t + 1 )}

Solution steps

\frac{d}{d t} (arctan (2 t))

Simplify

arctan (2 t) : arctan (2 t)

= \frac{d}{d t} (arctan (2 t))

Apply the chain rule:

\frac{1}{( 2 t ) ^{2} + 1} \frac{d}{d t} (2 t)

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

\frac{d}{d t} (2 t) = \frac{1}{2 t}

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

Simplify

\frac{1}{( 2 t ) ^{2} + 1} \cdot \frac{1}{2 t} : \frac{1}{2 t ( 2 t + 1 )}

= \frac{1}{2 t ( 2 t + 1 )}

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Frequently Asked Questions (FAQ)

What is the derivative of y=arctan(sqrt(2t)) ?
The derivative of y=arctan(sqrt(2t)) is 1/(sqrt(2)\sqrt{t)(2t+1)}
What is the first derivative of y=arctan(sqrt(2t)) ?
The first derivative of y=arctan(sqrt(2t)) is 1/(sqrt(2)\sqrt{t)(2t+1)}