What is (\partial)/(\partial x)(arcsin(6xyz)) ?

The answer to (\partial)/(\partial x)(arcsin(6xyz)) is (6yz)/(sqrt(1-36x^2y^2z^2))

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(\partial)/(\partial x)(arcsin(6xyz))

\frac{\partial}{\partial x} (arcsin (6 x yz))

\frac{6 yz}{1 - 36 x ^{2} y ^{2} z ^{2}}

Solution steps

\frac{\partial}{\partial x} (arcsin (6 x yz))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{1 - ( 6 x yz ) ^{2}} \frac{\partial}{\partial x} (6 x yz)

= \frac{1}{1 - ( 6 x yz ) ^{2}} \frac{\partial}{\partial x} (6 x yz)

\frac{\partial}{\partial x} (6 x yz) = 6 yz

= \frac{1}{1 - ( 6 x yz ) ^{2}} \cdot 6 yz

Simplify

\frac{1}{1 - ( 6 x yz ) ^{2}} \cdot 6 yz : \frac{6 yz}{1 - 36 x ^{2} y ^{2} z ^{2}}

= \frac{6 yz}{1 - 36 x ^{2} y ^{2} z ^{2}}

(3 t + 4) \cdot sin (π (\frac{t}{3} - 0.5))

y^{^{''}} - y^{^{'}} - 12 y = - 5, y (0) = 0, y^{^{'}} (0) = 0

x \to 2 - lim (\frac{x}{2 - x})

\int \frac{x ^{2}}{289 - x ^{2}} d x

\frac{d ^{2}}{d y ^{2}} (x y e^{(- x + 3 y)})

What is (\partial)/(\partial x)(arcsin(6xyz)) ?
The answer to (\partial)/(\partial x)(arcsin(6xyz)) is (6yz)/(sqrt(1-36x^2y^2z^2))