If d y d x = 2 x 3 , then find d x d y .

Given that, d y d x = 2 x 3 We know that, d x d y is nothing but, reciprocal of d y d x . Therefore, d x d y = 1 2 x 3

If d y d x = 2 x 3 , then find d x d y .

Given that, d y d x = 2 x 3 We know that, d x d y is nothing but, reciprocal of d y d x . Therefore, d x d y = 1 2 x 3

The differential of y if y = x 4 + x 2 + 1 is

1 2 x 4 + x 2 + 1 - 1 2 4 x 3 + 2 x d x

1 2 x 4 + x 2 + 1 - 1 2 4 x 3 + 2 x

EASY

Earn 100

If $\frac{d y}{d x} = 2 x^{3}$ , then find $\frac{d x}{d y}$ .

Important Questions on Differentiation

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

Find $\frac{d y}{d x}$ , where $y = \tan^{- 1} x + \cot^{- 1} x$ .

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

Let

f (x + y) = f (x) f (y)

for all

x

and

y .

f (4) = 3

and

f^{'} (0) = 1,

then

f^{'} (4)

equals.

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

The differential of $y$ if $y = \sqrt{x^{4} + x^{2} + 1}$ is

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

Y = x (x - 1) (x - 2)

then

d y / d x

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

Let $K$ be a set of real number and $f : K \to R$ such that for all $x$ and $y,$ $|f (x) - f (y)| \leq {|x - y|}^{5} .$

If $f (3) = 7,$ then the value of $f (9)$ is

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

Let

f : ℝ \to ℝ

be a nonconstant differentiable function such that

\lim_{x \to \infty} f (x) = 1

and

\lim_{x \to \infty} f^{'} (x) = α

for some

α \in R

. Then

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

How many functions

f : R \to R

satisfy

f (1) = 10

and

|f (x) - f (y)| = |x - y|

for all

x, y \in R ?

HARD

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

Let

f

be a differentiable function such that

f (1) = 2

and

f^{'} (x) = f (x)

for all

x \in R

. If

h (x) = f (f (x))

, then

h^{'} (1)

is equal to :

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

f (x + y) = f (x) f (y)

for all

x

and

y

and

f (5) = 2, f^{'} (0) = 3

, then

f^{'} (5)

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

S^{2} = a t^{2} + 2 bt + c

, then the acceleration is

HARD

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

Let

c, k \in R

. If

f (x) = (c + 1) x^{2} + (1 - c^{2}) x + 2 k

and

f (x + y) = f (x) + f (y) - x y

, for all

x, y \in R

, then the value of

|2 (f (1) + f (2) + f (3) + \dots \dots + f (20))|

is equal to ______.

HARD

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

a \neq b, x \neq n π, n \in Z

and

y^{2} = a^{2} \cos^{2} x + b^{2} \sin^{2} x,

then

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

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

Let

f : ℝ \to ℝ

be a differentiable function that satisfies the relation

f (x + y) = f (x) + f (y) - 1, \forall x

y \in ℝ

. If

f^{'} (0) = 2

, then

| f (- 2) |

is equal to

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

Differentiate

\sin x

by First Principle.

HARD

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

Let

f : R \to R, g : R \to R

and

h : R \to R

be differentiable functions such that

f (x) = x^{3} + 3 x + 2

g (f (x)) = x

and

h (g (g (x))) = x

for all

x \in R .

Then,

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

If for

x \in (0, \frac{1}{4}),

the derivative of

\tan^{- 1} (\frac{6 x \sqrt{x}}{1 - 9 x^{3}})

\sqrt{x} \cdot g (x)

, then

g (x)

equals:

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

y = \sec (\tan^{- 1} x)

, then

\frac{d y}{d x}

x = 1

is equal to

HARD

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

y = \tan x

, then

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

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

Let

y = f (x) = 2 x^{2} - 3 x + 2

. The differential of

y

when

x

changes from

2

1.99

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation using Chain Rule or Substitution

f

is differentiable at

x = 1

and

f (1) = 0,

\lim_{h \to 0} \frac{1}{h} f (1 + h) = 5,

then

f^{'} (1) =

If dydx=2x3, then find dxdy.

Important Questions on Differentiation

Learn and Prepare for any exam you want !

If $\frac{d y}{d x} = 2 x^{3}$ , then find $\frac{d x}{d y}$ .