Differentiate the following functions with respect to x using chain rule:

A) ?(a^2-x^2)/?(a^2+x^2)
B) sin ?x +cos^2?x
C)sin (ax+b)/cos (cx+d)

Question

Differentiate the following functions with respect to x using chain
rule:

A) ?(a^2-x^2)/?(a^2+x^2)
B) sin ?x +cos^2?x
C)sin (ax+b)/cos (cx+d)

Ankita Agarwal · Accepted Answer

Dear Student,

Solving by taking A part of your question as a2-x2a2+x2Let y = a2-x2a2+x2Let u = a2-x2a2+x2, Then y = uBy using chain rule, dydx = dydu×dudxDifferentiating u w
r
t x, we getdudx = -2xa2+x2-a2-x22xa2+x22dudx = -2xa2-2x3-2xa2+2x3a2+x22dudx = -4a2xa2+x22Now, y = udydu = 12uSo, dydx = dydu×dudxdydx =12u×-4a2xa2+x22Substitutig value of u, dydx = 12a2+x2a2-x2×-4a2xa2+x22dydx = -2a2x(a2-x2)12 (a2+x2)32

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Differentiate the following functions with respect to x using chain rule: A) ?(a^2-x^2)/?(a^2+x^2) B) sin ?x +cos^2?x C)sin (ax+b)/cos (cx+d)

Differentiate the following functions with respect to x using chain rule:

A) ?(a^2-x^2)/?(a^2+x^2)
B) sin ?x +cos^2?x
C)sin (ax+b)/cos (cx+d)