What is the d/(dt)(arcsin(sqrt(2t))) ?

The d/(dt)(arcsin(sqrt(2t))) is 1/(sqrt(2)\sqrt{t)sqrt(1-2t)}

What is the first d/(dt)(arcsin(sqrt(2t))) ?

The first d/(dt)(arcsin(sqrt(2t))) is 1/(sqrt(2)\sqrt{t)sqrt(1-2t)}

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

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

Solution steps

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

Simplify

arcsin (2 t) : arcsin (2 t)

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

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

Simplify

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

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

What is the d/(dt)(arcsin(sqrt(2t))) ?
The d/(dt)(arcsin(sqrt(2t))) is 1/(sqrt(2)\sqrt{t)sqrt(1-2t)}
What is the first d/(dt)(arcsin(sqrt(2t))) ?
The first d/(dt)(arcsin(sqrt(2t))) is 1/(sqrt(2)\sqrt{t)sqrt(1-2t)}