Differentiate the function 5 · e x with respect to x .

We want to find the derivative of 5 · e x . We know that d d y c · f y = c · d d y f y . . . 1 Clearly, d d x 5 · e x = 5 · d d x e x [Using 1 ] ⇒ d d x 5 · e x = 5 e x

Differentiate the function 5 · e x with respect to x .

We want to find the derivative of 5 · e x . We know that d d y c · f y = c · d d y f y . . . 1 Clearly, d d x 5 · e x = 5 · d d x e x [Using 1 ] ⇒ d d x 5 · e x = 5 e x

For x > 1 , if 2 x 2 y = 4 e 2 x - 2 y , then 1 + log e ⁡ 2 x 2 d y d x is equal to

x log e ⁡ 2 x - log e ⁡ 2 x

x log e ⁡ 2 x + log e ⁡ 2 x

EASY

Earn 100

Differentiate the function $5 \cdot e^{x}$ with respect to $x$ .

Important Questions on Differentiation

MEDIUM

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

Let

f (x) = \log_{e} (s i n x), (0 < x < π)

and

g (x) = \sin^{- 1} (e^{- x}), (x \geq 0) .

α

is a positive real number such that

a = {(f o g)}^{'} (α)

and

b = (f o g) (α),

then

MEDIUM

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

Let

f

and

g

be differentiable functions such that

f (3) = 5, g (3) = 7, f^{'} (3) = 13, g^{'} (3) = 6, f^{'} (7) = 2

and

g^{'} (7) = 0

.

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

then

h^{'} (3) =

HARD

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

Let

f (x) = x \sin π x, x > 0

. Then for all natural numbers

n, f^{'} (x)

vanishes at

MEDIUM

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

Given,

F (x) = (f (g (x)))^{2}, g (1) = 2, g^{'} (1) = 3, f (2) = 4

and

f' (2) = 5

, then the value of

F' (1)

is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

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

, then

\frac{d y}{d x}

x = 1

is equal to

EASY

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

y = 2 + \sqrt{u}

and

u = x^{3} + 1

, then

\frac{d y}{d x} =

EASY

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

Let

f : f (- x) \to f (x)

be a differentiable function. If

f

is even, then

f^{'} (0)

is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

For

x \neq - 1, y \neq - 1

, if

x = \frac{1 - \sqrt[3]{y}}{1 + \sqrt[3]{y}}

, then

\frac{d x}{d y} =

EASY

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

\sin y = x \sin (a + y)

, then

\frac{d y}{d x}

MEDIUM

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

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>General Theorems on Differentiation

(a + \sqrt{2} b \cos x) (a - \sqrt{2} b \cos y) = a^{2} - b^{2}

, where

a > b > 0,

then

\frac{d x}{d y}

(\frac{π}{4}, \frac{π}{4})

is:

EASY

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

For

x > 1

, if

{(2 x)}^{2 y} = 4 e^{2 x - 2 y}

, then

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

is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

y = \tan^{- 1} \frac{4 x}{1 + 5 x^{2}} + \tan^{- 1} \frac{2 + 3 x}{3 - 2 x},

then

\frac{d y}{d x} =

MEDIUM

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

Let

y = y (x)

be a function of

x

satisfying

y \sqrt{1 - x^{2}} = k - x \sqrt{1 - y^{2}}

, where

k

is a constant and

y (\frac{1}{2}) = - \frac{1}{4}

. Then

\frac{d y}{d x}

x = \frac{1}{2}

, is equal to

EASY

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

\sin y = x \sin (a + y)

, then

\frac{d y}{d x}

is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

\log_{10} (\frac{x^{3} - y^{3}}{x^{3} + y^{3}}) = 2

, then

\frac{d x}{d y} =

EASY

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

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

then

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

MEDIUM

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

g (x)

is the inverse function of

f (x)

and

f^{'} (x) = \frac{1}{1 + x^{4}},

then

g^{'} (x)

HARD

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

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 :

HARD

Mathematics>Differential Calculus>Differentiation>General Theorems on Differentiation

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,

Differentiate the function 5·ex with respect to x.

Important Questions on Differentiation

Learn and Prepare for any exam you want !

Differentiate the function $5 \cdot e^{x}$ with respect to $x$ .