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

The answer to (\partial)/(\partial x)((y+z)(arcsin(x))) is (y+z)/(sqrt(1-x^2))

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

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

\frac{y + z}{1 - x ^{2}}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= (y + z) \frac{\partial}{\partial x} (arcsin (x))

Apply the common derivative:

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

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

Simplify

(y + z) \frac{1}{1 - x ^{2}} : \frac{y + z}{1 - x ^{2}}

= \frac{y + z}{1 - x ^{2}}

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