What is the derivative of y=arcsin(sqrt(2)*t) ?

The derivative of y=arcsin(sqrt(2)*t) is sqrt(2/(1-2t^2))

What is the first derivative of y=arcsin(sqrt(2)*t) ?

The first derivative of y=arcsin(sqrt(2)*t) is sqrt(2/(1-2t^2))

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derivative of

y = arcsin (2 \cdot t)

\frac{2}{1 - 2 t ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2}{1 - 2 t ^{2}}

What is the derivative of y=arcsin(sqrt(2)*t) ?
The derivative of y=arcsin(sqrt(2)*t) is sqrt(2/(1-2t^2))
What is the first derivative of y=arcsin(sqrt(2)*t) ?
The first derivative of y=arcsin(sqrt(2)*t) is sqrt(2/(1-2t^2))