Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 6 - Differentiation>Target Exercises>Q 52

MEDIUM

JEE Advanced

IMPORTANT

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If $f (x)$ is a polynomial of degree $3$ such that $f (3) = 1, f^{'} (3) = - 1, f^{"} (3) = 0$ and $f^{'''} (3) = 12$ . Then, the value of $f^{'} (1)$ is

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Important Questions on Differentiation

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 6 - Differentiation>Target Exercises>Q 53

Let

f (x) = \sin x, g (x) = 2 x

and

h (x) = \cos x .

If

ϕ (x) = g [(f h) x]

, then

ϕ^{"} (\frac{π}{4})

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 6 - Differentiation>Target Exercises>Q 54

If the parametric equation of a curve is given by

x = \cos θ + logtan (\frac{θ}{2})

and

y = \sin θ,

then the points for which

\frac{d^{2} y}{d x^{2}} = 0,

are given by

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 6 - Differentiation>Target Exercises>Q 55

If

x^{2} + y^{2} = a^{2}

, then

a

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 6 - Differentiation>Target Exercises>Q 56

If

y = \tan^{- 1} [\frac{\log (\frac{e}{x^{3}})}{\log (e x^{3})}] + \tan^{- 1} [\frac{\log (e^{4} x^{3})}{\log (\frac{e}{x^{12}})}]

, then

\frac{d^{2} y}{d x^{2}}

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 6 - Differentiation>Target Exercises>Q 57

Let

f (x)

be a polynomial in

e^{x}

. Then, the second order derivative of

f (e^{x})

w.r.t.

x,

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 6 - Differentiation>Target Exercises>Q 58

Let

f (x) = \sin x, g (x) = x^{2}

and

h (x) = \log_{e} x

If

F (x) = (h o g o f) x,

then

F^{"} (x)

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 6 - Differentiation>Target Exercises>Q 59

The functions

u = e^{x} \sin x, v = e^{x} \cos x

satisfy the equation

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 6 - Differentiation>Target Exercises>Q 60

The derivative of

{cosec}^{- 1} (\frac{1}{2 x^{2} - 1})

w.r.t.

\sqrt{1 - x^{2}}

at

x = \frac{1}{2}

is equal to