# Find the Derivative – d/dx y=tan(arcsin(x)) 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.
One to any power is one.
Rewrite as .
Differentiate using the Quotient Rule which states that is where and .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify.
Differentiate using the Power Rule.
Differentiate using the Power Rule which states that is where .
Multiply by .
Differentiate using the chain rule, which states that is where and .
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 .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Combine fractions.
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 .
Since is constant with respect to , the derivative of with respect to is .
Multiply.
Multiply by .
Multiply by .
Differentiate using the Power Rule which states that is where .
Combine fractions.
Combine and .
Combine and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
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 .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply by by adding the exponents.
Use the power rule to combine exponents.
Combine the numerators over the common denominator.
Divide by .
Simplify .
Rewrite as a product.
Multiply and .
Multiply by by adding the exponents.
Multiply by .
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 .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .     