What is the derivative of arcsin(9x+9y) ?

The derivative of arcsin(9x+9y) is 9/(sqrt(1-81x^2-162xy-81y^2))

What is the first derivative of arcsin(9x+9y) ?

The first derivative of arcsin(9x+9y) is 9/(sqrt(1-81x^2-162xy-81y^2))

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derivative of

arcsin (9 x + 9 y)

\frac{9}{1 - 81 x ^{2} - 162 x y - 81 y ^{2}}

Solution steps

\frac{d}{d x} (arcsin (9 x + 9 y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{1 - ( 9 x + 9 y ) ^{2}} \frac{d}{d x} (9 x + 9 y)

= \frac{1}{1 - ( 9 x + 9 y ) ^{2}} \frac{d}{d x} (9 x + 9 y)

\frac{d}{d x} (9 x + 9 y) = 9

= \frac{1}{1 - ( 9 x + 9 y ) ^{2}} \cdot 9

Simplify

\frac{1}{1 - ( 9 x + 9 y ) ^{2}} \cdot 9 : \frac{9}{1 - 81 x ^{2} - 162 x y - 81 y ^{2}}

= \frac{9}{1 - 81 x ^{2} - 162 x y - 81 y ^{2}}

What is the derivative of arcsin(9x+9y) ?
The derivative of arcsin(9x+9y) is 9/(sqrt(1-81x^2-162xy-81y^2))
What is the first derivative of arcsin(9x+9y) ?
The first derivative of arcsin(9x+9y) is 9/(sqrt(1-81x^2-162xy-81y^2))