What is (\partial)/(\partial x)(arcsin(3x+y)) ?

The answer to (\partial)/(\partial x)(arcsin(3x+y)) is 3/(sqrt(1-9x^2-6xy-y^2))

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(\partial)/(\partial x)(arcsin(3x+y))

\frac{\partial}{\partial x} (arcsin (3 x + y))

\frac{3}{1 - 9 x ^{2} - 6 x y - y ^{2}}

Solution steps

\frac{\partial}{\partial x} (arcsin (3 x + y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{1 - ( 3 x + y ) ^{2}} \frac{\partial}{\partial x} (3 x + y)

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

\frac{\partial}{\partial x} (3 x + y) = 3

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

Simplify

\frac{1}{1 - ( 3 x + y ) ^{2}} \cdot 3 : \frac{3}{1 - 9 x ^{2} - 6 x y - y ^{2}}

= \frac{3}{1 - 9 x ^{2} - 6 x y - y ^{2}}

f (x) = 6 e^{x} cos (x)

y^{2} = x + 2, y^{2} = 2 - x

f (x) = - \frac{7}{( x - 7 ) ^{2}}

\int sin^{2} (\frac{2 π x}{L}) d x

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

What is (\partial)/(\partial x)(arcsin(3x+y)) ?
The answer to (\partial)/(\partial x)(arcsin(3x+y)) is 3/(sqrt(1-9x^2-6xy-y^2))