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

$\frac{d y}{d x}=2 x e^{x^{2}-1} \cos ^{-1} 2 x-\frac{2 e^{x^{2}-1}}{\sqrt{1-4 x^{2}}}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 6

Derivative of the Exponential Function

Derivatives

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Yeah. We want to find dy dx for the function why is equal to our coast or the inverse co sign of two X times E D x squared minus one to do this. So we're gonna rely on derivative shortcuts specifically. We're gonna rely on the left on zero G d X b D U and d d u l n g d x. GTX CTU is feeding the U d X on the right rules 123 of the power world products in general. I will also define the inverse coastline derivative as we get there. So why equals our coast to X T V x squared minus one is already written. It's easy different to perform such a procedure to derivative. We take the product rule to separate out derivatives derivatives for our coast to X and E x squared minus one. That's why the product or derivatives becomes dy dx equals on the left negative to over one minus four X squared times E to the x squared minus one. This is because the derivative of our coast of you is do you over one minus U squared on the right? We have plus coast negative +12 X m e x squared minus one times two X. This is my world zero. Thus making sure that we have everything in order or rather separating r e x squared minus one. We have final solution of the bottom. Dy dx equals e x squared minus one times two X. Art coast to x minus two over square one minus four X squared.

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