Question 20 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (a + bsinx) / (c + d cos x)
Class X1 - Maths -Limits and Derivatives Page 318
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y =(a + bsinx) / (c + d cos x)
using division rule
Differentiating w.r.t x
=>
dy/dx ={ (c+dcosx) d/dx(a+bsinx)-(a+bsinx)d/dx(c+dcosx) }/(c+dcosx)²
= (c+dcosx)(bcosx)-(a+bsinx)(-dsinx)/(c+dcosx)²
= (c+dcosx)(bcosx)+(a+bsinx)(dsinx)/(c+dcosx)²
using division rule
Differentiating w.r.t x
=>
dy/dx ={ (c+dcosx) d/dx(a+bsinx)-(a+bsinx)d/dx(c+dcosx) }/(c+dcosx)²
= (c+dcosx)(bcosx)-(a+bsinx)(-dsinx)/(c+dcosx)²
= (c+dcosx)(bcosx)+(a+bsinx)(dsinx)/(c+dcosx)²
Similar questions
using division rule
Differentiating w.r.t x
=>
dy/dx ={ (c+dcosx) d/dx(a+bsinx)-(a+bsinx)d/dx(c+dcosx) }/(c+dcosx)²
= (c+dcosx)(bcosx)-(a+bsinx)(-dsinx)/(c+dcosx)²
= (c+dcosx)(bcosx)+(a+bsinx)(dsinx)/(c+dcosx)