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17 votes
Differentiate y = 8x/ 3 − tan(x)

User Robert Siemer
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1 Answer

23 votes
23 votes

Answer:


(dy)/(dx)=(8(xsec^2(x)-tan(x)+3))/((3-tan(x))^2)

Explanation:


y=(8x)/(3-tan(x))\\ \\(dy)/(dx)=((3-tan(x))((d)/(dx)8x)-((d)/(dx)(3-tan(x)))(8x))/((3-tan(x))^2)\\ \\ (dy)/(dx)=((3-tan(x))(8)-(-sec^2(x))(8x))/((3-tan(x))^2)\\ \\ (dy)/(dx)=(24-8tan(x)+8xsec^2(x))/((3-tan(x))^2)\\ \\ (dy)/(dx)=(8xsec^2(x)-8tan(x)+24)/((3-tan(x))^2)\\\\ (dy)/(dx)=(8(xsec^2(x)-tan(x)+3))/((3-tan(x))^2)

Remember to use the Quotient Rule

User Gallly
by
2.9k points
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