What is the derivative of arcsin(8x) ?

The derivative of arcsin(8x) is 8/(sqrt(1-64x^2))

What is the first derivative of arcsin(8x) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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