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CGP EDU Academic Team
Published on: August 14, 2026
If y = 
dt let us define 
in different manner
= v'(x) f(v(x)) – u'(x) f(u(x)) and the equation of tangent at (a, b) as (y – b) = 
(x – a)
(i) If y = 
then equation of the tangent at x = 1 is
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Ans.
(i)
Sol. 
= 2x (x 4 ) – 1 (x 2 )
= 2 – 1 = 1
at x = 1 y = 
dt = 0
(y – 0) = 1 (x – 1)
⇒ y = x – 1
(ii)
Sol. f '(x) = 
(1 – x 2 ) = 0
[f '(x)] x = 1 = e(1 – 1) = 0
(iii)
Sol. 
= 4x 3 log (x 4 ) – 3x 2 log (x 3 )
= 
16 x 3 log (x) – 9x 2 log(x)
= 
– 
= 
– 
= 0 – 0 = 0
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