What is the derivative of arcsin(ax) ?

The derivative of arcsin(ax) is a/(sqrt(1-a^2x^2))

What is the first derivative of arcsin(ax) ?

The first derivative of arcsin(ax) is a/(sqrt(1-a^2x^2))

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

\frac{a}{1 - a ^{2} x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{1 - ( a x ) ^{2}} a : \frac{a}{1 - a ^{2} x ^{2}}

= \frac{a}{1 - a ^{2} x ^{2}}

\frac{( x + 9 )}{( x + 4 )}

3 sin (x), 0, 0.6 π, 4 cos (x)

y^{^{''}} + 9 y = e^{- t}

\int arcsin (cos (x)) d x

\int \frac{1}{( 16 + x ^{2} ) ^{2}} d x

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