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# Class 12 NCERT Solutions- Mathematics Part I – Chapter 5 Continuity And Differentiability – Exercise 5.2

### Question 1. Sin(x2 + 5)

Solution:

y = sin(x2 + 5) = = cos(x2 + 5) × = cos(x2 + 5) × (2x)

dy/dx = 2xcos(x2 + 5)

### Question 2. cos(sin x)

Solution:

y = cos(sin x) = = -sin(sin x) × = -sin(sin x)cos x

### Question 3. sin(ax + b)

Solution:

y = sin(ax + b)  = a cos(ax + b)

### Question 4. Sec(tan(√x)

Solution:

y = sec(tan√x) = = sec(tan √x) × tan(√x) × = sec (tan √x) × tan (tan √x) × sec2√x × = sec(tan√x)tan(tan√x)(sec2√x)1/(2√x)

= 1/(2√x) × sec(tan√x)tan(tan√x)(sec2√x)

### Question 5. Solution:

y =   = ### Question 6. cos x3.sin2(x5)

Solution:

y = cos x3.sin2(x5)  = cos x3.2sin(x5) .cos(x5(5x4)(5x4) – sin2(x5).sin x3.3x2

= 10x4 cos x3sin(x5)cos(x5) – 3x2 sin2(x5)sin x3

### Question 7. 2√(cos(x2))

Solution:

y = 2√(cos(x2)) = = 2    =        ### Question 8. cos (√x)

Solution:

y = cos (√x)

dy/dx = -sin√x = = ### Question 9. Prove that the function f given by f(x) = |x – 1|, x ∈ R is not differentiable at x = 1.

Solution:    = = +1     = -1

LHD ≠ RHD

Hence, f(x) is not differentiable at x = 1

### Question 10. Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.

Solution:

Given: f(x) = [x], 0 < x < 3

LHS:

f'(1) =  = = ∞

RHS:

f'(1) =    = 0

LHS ≠ RHS

So, the given f(x) = [x] is not differentiable at x = 1.

Similarly, the given f(x) = [x] is not differentiable at x = 2.

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