Class 12 CBSE Applied Maths Differentiation Exercise 5.2

Class 12 CBSE Applied Maths aims to develop an understanding of basic mathematical and statistical tools and their applications in the field of commerce (business/ finance/economics) and social sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index Numbers and Time-based data , Financial Mathematics , Linear Programming.


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Exercise 5.1 Exercise 5.3 Exercise 5.4

Q1. (i) (x + 3)2 (x + 4)3 (x + 5)4
(ii)
x √x2 + 1 / (x + 1)2/3
, x > 0

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Q2. (i) (2x + 3)x - 5, x > -
3 / 2

(ii) (log x)log x, x > 1

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Q3. (i) If y = xy, prove that x
dy / dx
=
y2 / 1 - y log x

(ii) If x = ex/y, prove that x
dy / dx
=
x - y / x log x

(iii) If xy= ex - y, prove that
dy / dx
=
log x / (log xe)2

(iv) If x16y9 = (x2 + y)17, prove that
dy / dx
=
2y / x

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Q4. Find the derivative of xx + ax + xa + aa for some fixed a > 0, x > 0.

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Q5. Differentiate xlog x + (log x)x w.r.t. x.

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Q6. Find
dy / dx
when :
(i) xyyx = ab (ii) xy + yx = log a (iii) xy = ex - y.

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Q7. If y = xxx....∞ prove that
dy / dx
=
y2 / x(1- y log x)

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