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Class 11 (FYJC / HSC)Commerce Mathematics & Statistics2026-27 Syllabus

Chapter 9 Differentiation Ex 9.1 Solutions

Complete Maharashtra State Board Balbharati & Yuvakbharati textbook solutions for Chapter 9 Differentiation Ex 9.1. Step-by-step solved exercises, numerical problems, and digest answers.

23 Solved Questions• 26 Diagrams• 504 words

Balbharati Maharashtra State Board11th Commerce Maths Solution Book PdfChapter 9 Differentiation Ex 9.1 Questions and Answers.

Maharashtra State Board 11th Commerce Maths Solutions Chapter 9 Differentiation Ex 9.1

I. Find the derivatives of the following functions w.r.t. x.

Question 1 Maharashtra Board Solution

x12

Solution & Step-by-Step Answer:

Let y = x12 Differentiating w.r.t. x, we get

Question 2 Maharashtra Board Solution

x-9

Solution & Step-by-Step Answer:

Let y = x-9 Differentiating w.r.t. x, we get

Question 3 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Let y = Differentiating w.r.t. x, we get

Question 4 Maharashtra Board Solution

7x√x

Solution & Step-by-Step Answer:

Question 5 Maharashtra Board Solution

35

Solution & Step-by-Step Answer:

Let y = 35 Differentiating w.r.t. x, we get …..[35 is a constant]

II. Differentiate the following w.r.t. x.

Question 1 Maharashtra Board Solution

x5 + 3x4

Solution & Step-by-Step Answer:

Let y = x5 + 3x4 Differentiating w.r.t. x, we get

Question 2 Maharashtra Board Solution

x√x + log x – ex

Solution & Step-by-Step Answer:

Let y = x√x + log x – ex = Differentiating w.r.t. x, we get

Question 3 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Let y = Differentiating w.r.t. x, we get

Question 4 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Let y = Differentiating w.r.t. x, we get

Question 5 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Let y =

III. Differentiate the following w.r.t. x.

Question 1 Maharashtra Board Solution

x3 log x

Solution & Step-by-Step Answer:

Let y = x3 log x Differentiating w.r.t. x, we get

Question 2 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Let y = Differentiating w.r.t. x, we get

Question 3 Maharashtra Board Solution

ex log x

Solution & Step-by-Step Answer:

Let y = ex log x Differentiating w.r.t. x, we get

Question 4 Maharashtra Board Solution

x3. 3x

Solution & Step-by-Step Answer:

Let y = x3. 3x Differentiating w.r.t. x, we get

IV. Find the derivatives of the following w.r.t. x.

Question 1 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 2 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 3 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 4 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 5 Maharashtra Board Solution

Solution & Step-by-Step Answer:

V. Find the derivatives of the following functions by the first principle:

Question 1 Maharashtra Board Solution

3x2 + 4

Solution & Step-by-Step Answer:

Let f(x) = 3x2 + 4 ∴ f(x + h) = 3(x + h)2 + 4 = 3(x2 + 2xh + h2) + 4 = 3x2 + 6xh + 3h2 + 4 By first principle, we get

Question 2 Maharashtra Board Solution

x√x

Solution & Step-by-Step Answer:

Let f(x) = x√x ∴ f(x + h) = By first principle, we get

Question 3 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Let f(x) = ∴ f(x + h) = By first principle, we get

Question 4 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Let f(x) = ∴ f(x + h) = By first principle, we get

Previous Chapter

Chapter 8 Continuity Miscellaneous Exercise 8

Chapter 9 Differentiation Ex 9.2