Differentiation of Implicit Functions MCQ Quiz in मराठी - Objective Question with Answer for Differentiation of Implicit Functions - मोफत PDF डाउनलोड करा

Calculation:

Given,

Differentiate implicitly w.r.t. :

Rearrange to collect :

Use to simplify:

∴ , independent of and .

Hence, the correct answer is Option 4.

Concept:

Calculation:

Given 2x + 2y = 2x+y

We know that 2^a+b = 2^a⋅ 2^b

⇒ 2^x + 2^y = 2^x ⋅ 2^y

⇒ 

⇒ 2^-y + 2^-x = 1  ..(1)

Differentiating the above equation with respect to x:

⇒ (-2^{- y} - 2^{- x}) log 2 = 0

⇒ 

⇒ 

⇒  = - 2^y + 1

⇒  = 1 - 2^y

The required value of   is 1 - 2^y .  

Calculation:

Given:

Differentiating the given equation with respect to x, we get:

⇒

⇒

⇒

⇒  

⇒

⇒

⇒

⇒

∴

Hence option 3 is correct

Calculation

Differentiate both sides with respect to x:

⇒

⇒

⇒

At (1, 0):

⇒

⇒

⇒

⇒

Substitute (1, 0) in the given equation:

⇒

⇒

⇒

⇒

⇒

Hence option 4 is correct

Given

y= 3e^2x + 2e^3x

Formula used

d(xⁿ)/dx = nx^n-1

Solution

⇒dy/dx = 3e^2x(2) + 2e^3x(3)

⇒dy/dx = 6(e^2x + e^3x)

⇒d²y/dx² = 6(2e^2x+3e^3x)

As asked in the question,

⇒   - 5  + 6y =

⇒ 12e^2x + 18e^3x − 30e^2x − 30e^3x + 18e^2x + 12e^3x

⇒ 0.

The correct option is 4.

Concept:

Chain Rule (Differentiation by substitution): If y is a function of u and u is a function of x

Calculation:

Given y2 + x2 + 3x + 5 = 0

Differentiating with respect to x, we get

2y  + 2x +3(1) + 0 = 0

2y + 2x + 3 = 0 

2y  = -(2x + 3)

Now at (0, -3)

 = 0.5