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Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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Fill in the Blanks

Q. 1. Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE and f '(x) = sin x2 , then  Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE ....................

Ans. Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solution. 

Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Q. 2. If fr (x), g (x), hr (x) r , r = 1, 2, 3 are polynomials in x such that fr(a) = gr (a) = hr(a), r = 1, 2, 3

Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

....................

Ans. 

Solution. 

Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Where fr(x), gr(x), hr(x), r = 1, 2, 3, are polynominals in x and hence differentiable and

fr(a) = gr(a) = hr(a), r = 1, 2, 3 … (2)

Differentiating eq. (1) with respect to x, we get

Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Using eq. (2) we get D1 = D2 = D3 = 0 [By the property of determinants that D = 0 if two rows in D are identical]
∴ F'  (a) = 0.


Q. 3. If f(x) = logx (ln x), then f '(x) at x = e is ....................

Ans. 1/e

Solution. Given that

Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Q. 4. The derivative of Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEat = 1/2 is .......

Ans. 4

Solution.

Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 5.  If f (x) = | x – 2 | and g(x) = f [f(x)], then g'(x) = .................... for x > 20

Ans. 1

Solution. f (x) = | x – 2 |
⇒ g (x) = f (f (x)) = | f (x) – 2 | as x > 20
= || x - 2| -2 | = |x - 2- 2| as x > 20 = | x – 4 |
= x – 4 as x > 20  
∴ g' (x) = 1


Q. 6. If xexy = y + sin2 x, then at x = 0, dy/dx = ......

Ans. 1

Solution. Given : xexy = y + sin2 x

Differentiating both sides w. r.to x, we get

Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


True/ False

Q. 1. The derivative of an even function is always an odd function.

Ans. T

Solution. Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE , which is an even function

Fill in the Blanks: Differentiation | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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