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Single Variable Calculus

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Moderate

Logarithmic Differentiation of Rational Function

SVCALC-EP8RC4

Find derivative of the function:

$$y=\frac{x^{1/4}}{\sqrt{x^2+1}}{(x+2)^5}$$

A

$\cfrac{x^{1/4}}{\sqrt{x^2+1}}{(x+2)^5}(\cfrac{1}{4x}+\cfrac{1}{2 (x^2+1)}-5\cfrac{1}{x+2})$

B

$\cfrac{x^{1/4}}{\sqrt{x^2+1}}{(x+2)^5}(\cfrac{1}{4x}-\cfrac{x}{x^2+1} +5\cfrac{1}{x+2})$

C

$\cfrac{1}{4x}+\cfrac{x}{x^2+1} -5\cfrac{1}{x+2}$

D

$\cfrac{x^{1/4}}{\sqrt{x^2+1}}{(x+2)^5}(\cfrac{1}{4x}+\cfrac{x}{x^2+1} +5\cfrac{1}{x+2})$