Q. 434.7( 3 Votes )

# <span lang="EN-US

Let f(x) = Cos (x2 + 1) ------------(i)

f(x + ∆x) = Cos [(x + ∆x)2 + 1] -------(ii)

Subtracting eq. (i) from eq. (ii),

f(x + ∆x) - f(x) = Cos [(x + ∆x)2 + 1] - Cos (x2 + 1)

Dividing both sides by ∆x,

As per the definition of differentiations,

Taking limits,

= -2 Sin (x2 + 1).1.(x) = -2x Sin (x2 + 1)

As

Hence, the required answer is -2x Sin (x2 + 1).

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