Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 2 - Differentiation>Proficiency in 'Differentiation' Exercise 1>Q 1

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If $y = a t^{2} + 2 b t + c$ and $t = a x^{2} + 2 b x + c,$ then $\frac{d^{3} y}{d x^{3}}$ equals to:

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Important Questions on Differentiation

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IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 2 - Differentiation>Proficiency in 'Differentiation' Exercise 1>Q 2

Differential coefficient of

{\{x^{\frac{l + m}{m - n}}\}}^{\frac{1}{n - l}} \cdot {\{x^{\frac{m + n}{n - l}}\}}^{\frac{1}{l - m}} \cdot {\{x^{\frac{n + l}{l - m}}\}}^{\frac{1}{m - n}}

with respect to

x

is:

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 2 - Differentiation>Proficiency in 'Differentiation' Exercise 1>Q 3

If

y = (A + B x) e^{m x} + {(m - 1)}^{- 2} e^{x}

, then

\frac{d^{2} y}{d x^{2}} - 2 m \frac{d y}{d x} + m^{2} y

is equal to:

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 2 - Differentiation>Proficiency in 'Differentiation' Exercise 1>Q 4

Given,

f (x) = - \frac{x^{3}}{3} + x^{2} s i n (\frac{3 a}{2}) - x s i n a \cdot s i n (2 a) - 5 a r c s i n (a^{2} - 8 a + 17),

then

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 2 - Differentiation>Proficiency in 'Differentiation' Exercise 1>Q 5

If

f

and

g

are differentiable functions such that

g^{'} (a) = 2

and

g (a) = b

and if

f o g

is an identity function, then

f^{'} (b)

has the value equal to

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 2 - Differentiation>Proficiency in 'Differentiation' Exercise 1>Q 6

The derivative of the function

f (x) = {c o s}^{- 1} \{\frac{1}{\sqrt{13}} (2 c o s x - 3 s i n x)\} + {s i n}^{- 1} \{\frac{1}{\sqrt{13}} (2 c o s x + 3 s i n x)\}

with respect to

\sqrt{1 + x^{2}}

at

x = \frac{3}{4}

is:

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 2 - Differentiation>Proficiency in 'Differentiation' Exercise 1>Q 7

If

f (x) = \sqrt{x + 2 \sqrt{2 x - 4}} + \sqrt{x - 2 \sqrt{2 x - 4}}

, then the value of

10 f^{'} (102^{+}),

is

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 2 - Differentiation>Proficiency in 'Differentiation' Exercise 1>Q 8

Let

y = l n {(1 + c o s x)}^{2}

, then the value of

\frac{d^{2} y}{d x^{2}} + \frac{2}{e^{y / 2}}

is equal to:

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 2 - Differentiation>Proficiency in 'Differentiation' Exercise 1>Q 9

If

f (x) = \frac{a + \sqrt{a^{2} - x^{2}} + x}{\sqrt{a^{2} - x^{2}} + a - x}

where

a > 0

and

x < a

, then

f^{'} (0)

has a value equal to: