What is (\partial)/(\partial x)(arcsin(10xyz)) ?

The answer to (\partial)/(\partial x)(arcsin(10xyz)) is (10yz)/(sqrt(1-100x^2y^2z^2))

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(\partial)/(\partial x)(arcsin(10xyz))

\frac{\partial}{\partial x} (arcsin (10 x yz))

\frac{10 yz}{1 - 100 x ^{2} y ^{2} z ^{2}}

Solution steps

\frac{\partial}{\partial x} (arcsin (10 x yz))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{1 - ( 10 x yz ) ^{2}} \frac{\partial}{\partial x} (10 x yz)

= \frac{1}{1 - ( 10 x yz ) ^{2}} \frac{\partial}{\partial x} (10 x yz)

\frac{\partial}{\partial x} (10 x yz) = 10 yz

= \frac{1}{1 - ( 10 x yz ) ^{2}} \cdot 10 yz

Simplify

\frac{1}{1 - ( 10 x yz ) ^{2}} \cdot 10 yz : \frac{10 yz}{1 - 100 x ^{2} y ^{2} z ^{2}}

= \frac{10 yz}{1 - 100 x ^{2} y ^{2} z ^{2}}

y = \frac{1 + x}{1 + e ^{x}}, (0, \frac{1}{2})

x \to 0 + lim (3 x ln (x))

3 x ln (15 x)

1 = - sin (x - y) \frac{d}{d x} (x - y)

x \to 6 lim (\frac{2 x + 7}{x + 3})

What is (\partial)/(\partial x)(arcsin(10xyz)) ?
The answer to (\partial)/(\partial x)(arcsin(10xyz)) is (10yz)/(sqrt(1-100x^2y^2z^2))