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Popular >

derivative of tan(arcsin(x))

Solution

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

Solution

\frac{1}{( 1 - x ^{2} ) ^{\frac{3}{2}}}

Solution steps

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

Apply the chain rule:

sec^{2} (arcsin (x)) \frac{d}{d x} (arcsin (x))

= sec^{2} (arcsin (x)) \frac{d}{d x} (arcsin (x))

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

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

Simplify

sec^{2} (arcsin (x)) \frac{1}{1 - x ^{2}} : \frac{1}{( 1 - x ^{2} ) ^{\frac{3}{2}}}

= \frac{1}{( 1 - x ^{2} ) ^{\frac{3}{2}}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of tan(arcsin(x)) ?
The derivative of tan(arcsin(x)) is 1/((1-x^2)^{3/2)}
What is the first derivative of tan(arcsin(x)) ?
The first derivative of tan(arcsin(x)) is 1/((1-x^2)^{3/2)}