What is (\partial)/(\partial x)(arcsin(5xyz)) ?

The answer to (\partial)/(\partial x)(arcsin(5xyz)) is (5yz)/(sqrt(1-25x^2y^2z^2))

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(\partial)/(\partial x)(arcsin(5xyz))

\frac{\partial}{\partial x} (arcsin (5 x yz))

\frac{5 yz}{1 - 25 x ^{2} y ^{2} z ^{2}}

Solution steps

\frac{\partial}{\partial x} (arcsin (5 x yz))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{1 - ( 5 x yz ) ^{2}} \frac{\partial}{\partial x} (5 x yz)

= \frac{1}{1 - ( 5 x yz ) ^{2}} \frac{\partial}{\partial x} (5 x yz)

\frac{\partial}{\partial x} (5 x yz) = 5 yz

= \frac{1}{1 - ( 5 x yz ) ^{2}} \cdot 5 yz

Simplify

\frac{1}{1 - ( 5 x yz ) ^{2}} \cdot 5 yz : \frac{5 yz}{1 - 25 x ^{2} y ^{2} z ^{2}}

= \frac{5 yz}{1 - 25 x ^{2} y ^{2} z ^{2}}

\int e^{3 x} x d x

n = 0 \sum \infty \frac{1}{n + 2}

\int \frac{9 - x ^{2}}{3 x} d x

sec (sin (x))

\frac{d S}{d t} = 0.9 - \frac{15 S}{1000}

What is (\partial)/(\partial x)(arcsin(5xyz)) ?
The answer to (\partial)/(\partial x)(arcsin(5xyz)) is (5yz)/(sqrt(1-25x^2y^2z^2))