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Find the derivatives of the given functions.$$y=\left(x^{2}+1\right) \sin ^{-1} 4 x$$

$\frac{d y}{d x}=\frac{4\left(x^{2}+1\right)}{\sqrt{1-16 x^{2}}}+2 x \sin ^{-1} 4 x$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 3

Derivatives of the Inverse Trigonometric Functions

Derivatives

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Yeah, we want to find the derivative dy dx for the function Y equals x squared plus one times the arc sine of forex to do so we're going to rely on derivative shortcuts. We picked up to a single variable calculus in particular the anniversary derivatives given here particularly we need to use the arc sine derivative D d x x and X equals 1/1 minus x squared will also need the both the channel and the product rule. So why is already written? It's most easily defensible form. We proceed to solve by first using the product rule on X squared plus one and arcs in forex separately. So do I. D. X is to wax works in forex. This is a derivative expert +12 X plus X squared plus one times for over route one of 16 X square. This is the derivative arcs in forex simplifying the term on the right. It gives us the expression of the box down here, which is do I D X equals two X. Mark signed for X plus four times X squared plus one over root one minus 16 X squared

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