What is the derivative of f(t)=arcsin(8t) ?

The derivative of f(t)=arcsin(8t) is 8/(sqrt(1-64t^2))

What is the first derivative of f(t)=arcsin(8t) ?

The first derivative of f(t)=arcsin(8t) is 8/(sqrt(1-64t^2))

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derivative of

f (t) = arcsin (8 t)

\frac{8}{1 - 64 t ^{2}}

Solution steps

\frac{d}{d t} (arcsin (8 t))

Apply the chain rule:

\frac{1}{1 - ( 8 t ) ^{2}} \frac{d}{d t} (8 t)

= \frac{1}{1 - ( 8 t ) ^{2}} \frac{d}{d t} (8 t)

\frac{d}{d t} (8 t) = 8

= \frac{1}{1 - ( 8 t ) ^{2}} \cdot 8

Simplify

\frac{1}{1 - ( 8 t ) ^{2}} \cdot 8 : \frac{8}{1 - 64 t ^{2}}

= \frac{8}{1 - 64 t ^{2}}

y = (x^{2} + 1)^{3} (x - 1)

\int e^{\frac{1}{2 x}} d x

\int \frac{1}{576 + x ^{2}} d x

\int arcsin^{2} (x) d x

\int \frac{1}{x ^{2} + 6 x + 25} d x

What is the derivative of f(t)=arcsin(8t) ?
The derivative of f(t)=arcsin(8t) is 8/(sqrt(1-64t^2))
What is the first derivative of f(t)=arcsin(8t) ?
The first derivative of f(t)=arcsin(8t) is 8/(sqrt(1-64t^2))