Class 12 CBSE Applied Maths Differentiation Exercise 5.4

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 5.2 Exercise 5.3

Q1. the second order derivatives of the following functions :
(i) x2+3x+2
(ii) x3 - 5x2+3x4+4
(iii) log x
(iv) log (log x)
(v)
log x / x

(vi)
2x + 1 / 2x + 3
(vii) √( 1 - x2)

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Q2. (i) If y = aemx + be-mx, prove that y2 - m2y = 0.
(ii) If y=500e7x + 600e-7x, prove that
d2y / dx2
= 49y
(iii) If y = ae2x + be-x prove that ,
d2y / dx2
-
dy / dx
- 2y = 0

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Q3. (i) If y =log (x + √x2 +1), prove that (x2 + 1)
d2y / dx2
+ x
dy / dx
= 0
(ii) If y = log (x + √x2 + a2), prove that (x2 + a2) y2 + xy1 = 0.

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Q4. If
x2 / a2
+
y2 / b2
= 1 prove that
d2y / dx2
= -
b4 / a2y3

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Q5. If x = log t and y = 1/t prove that
d2y / dx2
+
dy / dx
= 0

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Q6. If x = a(t + 1/t) and y = a(t - 1/t) show that y2
d2y / dx2
+ x
dy / dx
- y = 0

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Q7. If x = at2, y = 2at, find
d2y / dx2
at t = 3

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