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Popular >

derivative of y=tan(arcsin(x))

Solution

derivative of

y = tan (arcsin (x))

Solution

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

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

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y^'=0.2ln((3000)/y)y,y(0)=1000

y^{^{'}} = 0.2 ln (\frac{3000}{y}) y, y (0) = 1000

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Frequently Asked Questions (FAQ)

What is the derivative of y=tan(arcsin(x)) ?
The derivative of y=tan(arcsin(x)) is 1/((1-x^2)sqrt(1-x^2))
What is the first derivative of y=tan(arcsin(x)) ?
The first derivative of y=tan(arcsin(x)) is 1/((1-x^2)sqrt(1-x^2))