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Test: Differentiation Of Exponential Functions - JEE MCQ


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10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Differentiation Of Exponential Functions

Test: Differentiation Of Exponential Functions for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Differentiation Of Exponential Functions questions and answers have been prepared according to the JEE exam syllabus.The Test: Differentiation Of Exponential Functions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Differentiation Of Exponential Functions below.
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Test: Differentiation Of Exponential Functions - Question 1

The dervative of y 

Test: Differentiation Of Exponential Functions - Question 2

Differentiate   with respect to x.

Detailed Solution for Test: Differentiation Of Exponential Functions - Question 2

y = e^(-x)2.................(1)
Put u = (-x)2
du/dx = -2x dx
Differentiating eq(1) y = eu
dy/du = e^u
⇒ dy/dx = (dy/du) * (du/dx)
= (eu) * (-2x)
⇒ - 2xe(-x2)

Test: Differentiation Of Exponential Functions - Question 3

The derivatve of f(x) = 

Detailed Solution for Test: Differentiation Of Exponential Functions - Question 3

f(x) =   elog(logx3)
As log and e are inverse operations, therefore
f(x)= logx3
So derivative will be                         {Derivative of log x is 1/x and then applying chain rule}

f’(x)=1/x3. 3x= 3/x

Test: Differentiation Of Exponential Functions - Question 4

The sum of Which series is denoted by e.

Test: Differentiation Of Exponential Functions - Question 5

Derivatve of f(x)   is given by

Detailed Solution for Test: Differentiation Of Exponential Functions - Question 5

 y
The derivative of y = ef(x)is dy/dx = f'(x)ef(x)
In this case, f(x) = x2 , and the derivative of x2 = 2x
Therefore, f'(x)= 2x,
 dy/dx = 2x

Test: Differentiation Of Exponential Functions - Question 6

The differential equation of y = 

Test: Differentiation Of Exponential Functions - Question 7

If f(x) = e2x-5, then f'(x) is​

Test: Differentiation Of Exponential Functions - Question 8

Whta is the derivatve of y = log5 (x)

Detailed Solution for Test: Differentiation Of Exponential Functions - Question 8

y = log5 x = ln x/ln 5 → change of base 
= ln x/ln 5
dy/dx = 1/ln5⋅1/x → 1/ln5 is a constant, so we don't change it
= 1/(x ln 5)

Test: Differentiation Of Exponential Functions - Question 9

For what values of x is elogx = x

Detailed Solution for Test: Differentiation Of Exponential Functions - Question 9

The correct option is A
Set of all positive real numbers

Test: Differentiation Of Exponential Functions - Question 10

If f(x) = ex, then the value of f'(-3) is

Detailed Solution for Test: Differentiation Of Exponential Functions - Question 10

As, f (x) = ex
Similarly, f (-3) = e-3

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