Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.6

Students can download 11th Business Maths Chapter 5 Differential Calculus Ex 5.6 Questions and Answers, Notes, Samcheer Kalvi 11th Business Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 11th Business Maths Solutions Chapter 5 Differential Calculus Ex 5.6

Samacheer Kalvi 11th Business Maths Differential Calculus Ex 5.6 Text Book Back Questions and Answers

Question 1.
Find \(\frac{d y}{d x}\) for the following functions:
(i) xy – tan(xy)
(ii) x² – xy + y² = 1
(iii) x³ + y³ + 3axy = 1
Solution:
(i) Given xy = tan(xy)
Differentiating both sides with respect to x, we get

(ii) x² – xy + y² = 7
Differentiating both side with respect to x,

(iii) x³ + y³ + 3axy = 1
Differentiating both sides with respect to x,

Question 2.
If \(x \sqrt{1+y}+y \sqrt{1+x}=0\) and x ≠ y, then prove that \(\frac{d y}{d x}=-\frac{1}{(x+1)^{2}}\).
Solution:
Given \(x \sqrt{1+y}+y \sqrt{1+x}=0\)
\(x \sqrt{1+y}=-y \sqrt{1+x}\)
Squaring both sides we get
⇒ x² (1 + y) = y² (1 + x)
⇒ x² + x²y = y² + y²x
⇒ x² – y² + x²y – y²x = 0
⇒ (x + y) (x – y) + xy(x – y) = 0
⇒ (x – y) [(x + y) + xy] = 0
∴ x – y = 0 (or) x + y + xy = 0
x = y (or) x + y + xy = 0
Given that x ≠ y
x + y + xy = 0
⇒ y + xy = -x
⇒ y(1 + x) = -x

Hence proved.

Question 3.
If 4x + 3y = log(4x – 3y), then find \(\frac{d y}{d x}\)
Solution:
Given 4x + 3y = log(4x – 3y)
Differentiating both sides with respect to x,