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

The derivative of y=arccot(sqrt(t)) is -1/(2sqrt(t)(t+1))

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

The first derivative of y=arccot(sqrt(t)) is -1/(2sqrt(t)(t+1))

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derivative of

y = arccot (t)

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

Solution steps

\frac{d}{d t} (arccot (t))

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{''}} + 200 y^{^{'}} + 10 y = 100

\frac{d}{d x} (\frac{2 x}{x + 7})

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

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

\int_{0}^{2} (y - 1) (2 y + 1) d y

What is the derivative of y=arccot(sqrt(t)) ?
The derivative of y=arccot(sqrt(t)) is -1/(2sqrt(t)(t+1))
What is the first derivative of y=arccot(sqrt(t)) ?
The first derivative of y=arccot(sqrt(t)) is -1/(2sqrt(t)(t+1))