If x 2 + y 2 = 1 , then

y y ′ ′ - 2 y ′ 2 + 1 = 0

y y ′ ′ + 2 y ′ 2 + 1 = 0

Let f 1 ( x ) = e x , f 2 ( x ) = e f 1 ( x ) , … … f n + 1 ( x ) = e f n ( x ) for all n ≥ 1 . Then for any fixed n , d d x f n ( x ) is

f n ( x ) f n - 1 ( x ) … f 1 ( x )

Let C θ = ∑ n = 0 ∞ cos n θ n ! Which of the following statements is FALSE?

C ′ θ ≠ 0 for all θ ∈ R

HARD

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Let $y = \log_{e} (\frac{1 - x^{2}}{1 + x^{2}}), - 1 < x < 1$ . Then at $x = \frac{1}{2}$ , the value of $225 (y^{'} - y^{"})$ is equal to

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Important Questions on Differentiation

EASY

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

If $e^{y} (x + 1) = 1$ , then $\frac{d^{2} y}{d x^{2}} =$

HARD

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

y = e^{n x}

, then

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

is equal to :

HARD

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

y^{2} + \log_{e} (\cos^{2} x) = y, x \in (- \frac{π}{2}, \frac{π}{2})

then :

EASY

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

y = 2 x^{n + 1} + \frac{3}{x^{n}}

, then

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

MEDIUM

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

x + y = \tan^{- 1} y

and

y^{″} = f (y) y^{'},

then

f (y) =

HARD

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

a x^{2} + 2 h x y + b y^{2} = 0,

then

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

EASY

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

x = a \sec^{2} θ, y = a \tan^{2} θ

then

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

HARD

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

x = \log t, y + 1 = \frac{1}{t}

, then

e^{- x} \frac{d^{2} x}{d y^{2}} + \frac{d x}{d y} =

MEDIUM

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

y = {[x + \sqrt{x^{2} - 1}]}^{15} + {[x - \sqrt{x^{2} - 1}]}^{15}

, then

(x^{2} - 1) \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x}

is equal to

HARD

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

2 x = y^{\frac{1}{5}} + y^{- \frac{1}{5}}

and

(x^{2} - 1) \frac{d^{2} y}{d x^{2}} + λ x \frac{d y}{d x} + k y = 0

, then

λ + k

is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

y = \frac{{(\sin^{- 1} x)}^{2}}{2}

, then

(1 - x^{2}) y_{2} - x y_{1} =

MEDIUM

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

x^{2} + y^{2} = 1

, then

EASY

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

y = e^{4 x} \cos 5 x,

then

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

x = 0

HARD

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

x = e^{t} \sin t

and

y = e^{t} \cos t

t

is a parameter, then the value of

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

t = 0,

EASY

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

y = 3 e^{5 x} + 5 e^{3 x}

, then

\frac{d^{2} y}{d x^{2}} - 8 \frac{d y}{d x} =

MEDIUM

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

y = \sin m x,

then the value of the determinant

|\begin{matrix} y & y_{1} & y_{2} \\ y_{3} & y_{4} & y_{5} \\ y_{6} & y_{7} & y_{8} \end{matrix}|

, where

y_{n} = \frac{d^{n} y}{d x^{n}}

, is

HARD

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

Let

f_{1} (x) = e^{x}, f_{2} (x) = e^{f_{1} (x)}, \dots \dots

f_{n + 1} (x) = e^{f_{n} (x)}

for all

n \geq 1

. Then for any fixed

n, \frac{d}{d x} f_{n} (x)

MEDIUM

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

Let

C (θ) = \sum_{n = 0}^{\infty} \frac{\cos (n θ)}{n!}

Which of the following statements is FALSE?

HARD

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

\cos^{- 1} (\frac{y}{b}) = \log (\frac{x}{n}),

then

x^{2} y_{2} + x y_{1} =

MEDIUM

Mathematics>Differential Calculus>Differentiation>Higher Order Derivatives

f (x) = x^{n}

, then the value of

f (1) - \frac{f^{'} (1)}{1!} + \frac{f^{''} (1)}{2!} - \frac{f^{'''} (1)}{3!} + \dots + \frac{{(- 1)}^{n} f^{n} (1)}{n!}

Let y=loge1-x21+x2,-1<x<1. Then at x=12, the value of 225y'-y" is equal to

Important Questions on Differentiation

Learn and Prepare for any exam you want !

Let $y = \log_{e} (\frac{1 - x^{2}}{1 + x^{2}}), - 1 < x < 1$ . Then at $x = \frac{1}{2}$ , the value of $225 (y^{'} - y^{"})$ is equal to