What is (\partial)/(\partial x)(arcsin(11xyz)) ?

The answer to (\partial)/(\partial x)(arcsin(11xyz)) is (11yz)/(sqrt(1-121x^2y^2z^2))

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(\partial)/(\partial x)(arcsin(11xyz))

\frac{\partial}{\partial x} (arcsin (11 x yz))

\frac{11 yz}{1 - 121 x ^{2} y ^{2} z ^{2}}

Solution steps

\frac{\partial}{\partial x} (arcsin (11 x yz))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{1 - ( 11 x yz ) ^{2}} \frac{\partial}{\partial x} (11 x yz)

= \frac{1}{1 - ( 11 x yz ) ^{2}} \frac{\partial}{\partial x} (11 x yz)

\frac{\partial}{\partial x} (11 x yz) = 11 yz

= \frac{1}{1 - ( 11 x yz ) ^{2}} \cdot 11 yz

Simplify

\frac{1}{1 - ( 11 x yz ) ^{2}} \cdot 11 yz : \frac{11 yz}{1 - 121 x ^{2} y ^{2} z ^{2}}

= \frac{11 yz}{1 - 121 x ^{2} y ^{2} z ^{2}}

\frac{d}{d x} (\frac{5 x}{4 x ^{2} + 1})

e^{x} sin (x) + cos (x) e^{x}

f (x) = \frac{1}{4 - x ^{2}}

\int_{1}^{4} 3 x - 6 d x

What is (\partial)/(\partial x)(arcsin(11xyz)) ?
The answer to (\partial)/(\partial x)(arcsin(11xyz)) is (11yz)/(sqrt(1-121x^2y^2z^2))