Find the Derivative – d/dx y=tan(arcsin(x))

Math
Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .
Simplify the expression.
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One to any power is one.
Rewrite as .
Differentiate using the Quotient Rule which states that is where and .
Multiply the exponents in .
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Apply the power rule and multiply exponents, .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify.
Differentiate using the Power Rule.
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Differentiate using the Power Rule which states that is where .
Multiply by .
Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Combine fractions.
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Move the negative in front of the fraction.
Combine and .
Move to the denominator using the negative exponent rule .
Combine and .
By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Since is constant with respect to , the derivative of with respect to is .
Multiply.
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Multiply by .
Multiply by .
Differentiate using the Power Rule which states that is where .
Combine fractions.
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Combine and .
Combine and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Cancel the common factor.
Rewrite the expression.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply by by adding the exponents.
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Use the power rule to combine exponents.
Combine the numerators over the common denominator.
Add and .
Divide by .
Simplify .
Add and .
Add and .
Rewrite as a product.
Multiply and .
Multiply by by adding the exponents.
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Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps…
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Add and .
Reorder terms.
Find the Derivative – d/dx y=tan(arcsin(x))

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