What is the derivative of y=arctan(sqrt(4t)) ?

The derivative of y=arctan(sqrt(4t)) is 1/(sqrt(t)(4t+1))

What is the first derivative of y=arctan(sqrt(4t)) ?

The first derivative of y=arctan(sqrt(4t)) is 1/(sqrt(t)(4t+1))

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derivative of

y = arctan (4 t)

\frac{1}{t ( 4 t + 1 )}

Solution steps

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

Simplify

arctan (4 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}{t}

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

Simplify

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

= \frac{1}{t ( 4 t + 1 )}

x \to 2 + lim (\frac{4 x}{x - 2})

x y^{^{'}} - 2 y = x^{2} - 2 x - 1

\frac{\partial}{\partial x} (cot (x y))

\frac{1}{( 1 - x )}, 2

\int \frac{x ^{2} - 19}{x ^{3} - 2 x ^{2} + x} d x

What is the derivative of y=arctan(sqrt(4t)) ?
The derivative of y=arctan(sqrt(4t)) is 1/(sqrt(t)(4t+1))
What is the first derivative of y=arctan(sqrt(4t)) ?
The first derivative of y=arctan(sqrt(4t)) is 1/(sqrt(t)(4t+1))