What is (\partial)/(\partial x)(tan(x)arcsin(x)) ?

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

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(\partial)/(\partial x)(tan(x)arcsin(x))

\frac{\partial}{\partial x} (tan (x) arcsin (x))

sec^{2} (x) arcsin (x) + \frac{tan ( x )}{1 - x ^{2}}

Solution steps

\frac{\partial}{\partial x} (tan (x) arcsin (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = tan (x), g = arcsin (x)

= \frac{\partial}{\partial x} (tan (x)) arcsin (x) + \frac{\partial}{\partial x} (arcsin (x)) tan (x)

\frac{\partial}{\partial x} (tan (x)) = sec^{2} (x)

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

= sec^{2} (x) arcsin (x) + \frac{1}{1 - x ^{2}} tan (x)

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

= sec^{2} (x) arcsin (x) + \frac{tan ( x )}{1 - x ^{2}}

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