Answer to Question #265850 in Calculus for chaitu

Question

Lecture Notes of Athithan S

18MAB101T-Assignment-U2&3 S. Athithan

18MAB101T-Assignment-U2&3

Register No. :

Name :

Subject : 18MAB101T-Assignment-U2&3

Class/Room No. : Online/Online

Sem./Branch : I/CSE

Instructions:

Answer all the questions. Do the assignment neatly in the A4 sheets either writing or

typing and then scan it then submit to me through the Google Classroom. To follow the

uniformity you can print the above details in the front page of your assignment.

Questions to solve:

Unit-2

1. Find the total differential coefficient of the function u = tan (3x − y) + 5y+z

2. Find

dy

dx

if 4x

2 + y

3 + 5x

2y

5 = 7x

4y

2 − 2x + 9y − 3

Answer 1

1.

$$u_x=\dfrac{3}{\cos^2(x-y)}$$

$$u_y=-\dfrac{1}{\cos^2(x-y)}+5$$

$$u_z=1$$

$$du=(\dfrac{3}{\cos^2(x-y)})dx+(-\dfrac{1}{\cos^2(x-y)}+5)dy$$

$$+(1)dz$$

2.

$$4x^2+y^3+5x^2y^5=7x^4y^2-2x+9y-3$$

Differentiate both sides with respect to $x$ and use the Chain Rule

$$8x+3y^2\dfrac{dy}{dx}+10xy^5+25x^2y^4\dfrac{dy}{dx}$$

$$=28x^3y^2+14x^4y\dfrac{dy}{dx}-2+9\dfrac{dy}{dx}$$

Solve for $\dfrac{dy}{dx}$

$$\dfrac{dy}{dx}=\dfrac{8x+10xy^5-28x^3y^2+2}{14x^4y+9-3y^2-25x^2y^4}$$