Obtain dy/dx of x²+2/x³+5

Asked by innocentshah178 | 10th Nov, 2021, 11:57: PM

Expert Answer:

Let y = u / v
 
Then dy/dx is given as
 
begin mathsize 14px style fraction numerator d y over denominator d x end fraction space equals space fraction numerator v begin display style fraction numerator d u over denominator d x end fraction end style minus u begin display style fraction numerator d v over denominator d x end fraction end style over denominator v squared end fraction end style................................... (1)
begin mathsize 14px style y space equals space u over v space equals space fraction numerator x squared plus space 2 over denominator x cubed plus 5 end fraction end style
du/dx = 2x     ; dv/dx = 3 x2
 
then we get
 
begin mathsize 14px style fraction numerator d y over denominator d x end fraction space equals space fraction numerator left parenthesis x cubed plus 5 right parenthesis space left parenthesis 2 x right parenthesis space minus space left parenthesis x squared plus 2 right parenthesis left parenthesis 3 x squared right parenthesis over denominator left parenthesis space x cubed plus 5 space right parenthesis squared end fraction space equals space fraction numerator negative x to the power of 4 minus 6 space x squared plus 10 x over denominator left parenthesis x cubed plus 5 right parenthesis squared end fraction end style

Answered by Thiyagarajan K | 11th Nov, 2021, 08:21: AM