What is the derivative of y=arccot(sqrt(7t)) ?

The derivative of y=arccot(sqrt(7t)) is -(sqrt(7))/(2sqrt(t)(7t+1))

What is the first derivative of y=arccot(sqrt(7t)) ?

The first derivative of y=arccot(sqrt(7t)) is -(sqrt(7))/(2sqrt(t)(7t+1))

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derivative of

y = arccot (7 t)

- \frac{7}{2 t ( 7 t + 1 )}

Solution steps

\frac{d}{d t} (arccot (7 t))

Simplify

arccot (7 t) : arccot (7 t)

= \frac{d}{d t} (arccot (7 t))

Apply the chain rule:

- \frac{1}{( 7 t ) ^{2} + 1} \frac{d}{d t} (7 t)

= - \frac{1}{( 7 t ) ^{2} + 1} \frac{d}{d t} (7 t)

\frac{d}{d t} (7 t) = \frac{7}{2 t}

= - \frac{1}{( 7 t ) ^{2} + 1} \cdot \frac{7}{2 t}

Simplify

- \frac{1}{( 7 t ) ^{2} + 1} \cdot \frac{7}{2 t} : - \frac{7}{2 t ( 7 t + 1 )}

= - \frac{7}{2 t ( 7 t + 1 )}

\frac{d}{d x} (\frac{x}{x - y})

\frac{d}{d x} (- \frac{81}{x ^{4}})

\int 1 + 6 x^{\frac{1}{2}} d x

f (x) = x \cdot sin (x)

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (1) = 0, y^{^{'}} (1) = 3

What is the derivative of y=arccot(sqrt(7t)) ?
The derivative of y=arccot(sqrt(7t)) is -(sqrt(7))/(2sqrt(t)(7t+1))
What is the first derivative of y=arccot(sqrt(7t)) ?
The first derivative of y=arccot(sqrt(7t)) is -(sqrt(7))/(2sqrt(t)(7t+1))