### CBSE Assignments class 09 Mathematics

Mathematics Assignments & Worksheets  For  Class IX Chapter-wise mathematics assignment for class 09. Important and useful extra questions strictly according to the CBSE syllabus and pattern with answer key CBSE Mathematics is a very good platform for the students and is contain the assignments for the students from 9 th  to 12 th  standard.  Here students can find very useful content which is very helpful to handle final examinations effectively.  For better understanding of the topic students should revise NCERT book with all examples and then start solving the chapter-wise assignments.  These assignments cover all the topics and are strictly according to the CBSE syllabus.  With the help of these assignments students can easily achieve the examination level and  can reach at the maximum height. Class 09 Mathematics    Assignment Case Study Based Questions Class IX

### Math Assignment Class XII Ch-5 | Derivatives

Math Assignment Class XII Chapter 5 Derivatives

Question 1 Use chain rule to find the derivative of $y=\left ( \frac{2x-1}{2x+1} \right )^{2} \;\;\; Ans.1: \frac{8(2x-1)}{(2x+1)^{3}}$

Question 2Differentiate the following w.r.t. x $y=log_{10}x+ log_{x}10+log_{x}x+ log_{10}10$ Answer 2 $\frac{dy}{dx}=\frac{1}{xlog10}-\frac{log10}{x(logx)^{2}}$ Hint for the solution: $\frac{logx}{log10}+\frac{log10}{logx}+\frac{logx}{logx}+\frac{log10}{log10}$$=\frac{logx}{log10}+\frac{log10}{logx}+1+1$ Now differentiating w. r. t. x and taking log10 as constant.

Question 3. Differentiate the following w. r. t. x at x = 1$y=e^{x(1+logx)}\; \; \; \; \; \; \; \;........\: \: Ans.[2e]$
Question 4. $If\: \frac{x}{x-y}=log\frac{a}{x-y},\: then\: prove\: that\: \frac{dy}{dx}=\frac{2y-x}{y}$
Question 5: Differentiate log(x ex)  w. r. t.   xlogx.
Answer 5: $\frac{1+x}{x(1+logx)}$
Question 6: Differentiate x2 w. r. t. x3.        ...........    Ans:  2/3x.
Question 7: $If\: e^{x}+e^{y}=e^{x+y}, prove\: that\: \: \frac{dy}{dx}+e^{y-x}=0$ Solution 7: $e^{x}+e^{y}=e^{x+y}\\\frac{e^{x}}{e^{x+y}}+\frac{e^{y}}{e^{x}+e^{y}}=1\Rightarrow e^{-y}+e^{-x}=1$Now differentiating w. r. t. x we get the required answer.
Question 8: Differentiate  (xx) w. r. t. x
Answer 8: $\frac{dy}{dx}=x^{x^{2}}[x+2xlogx]...[Hint:(x^{x})^{x}=x^{x^{2}}]$
Question9.   Differentiate x16y9 = (x2 + y)17 w. r. t. x ,
Answer 9:  $\frac{dy}{dx}=\frac{2y}{x}$
Question10) Differentiate  (logx)x + xlogx, w. r. t. x.
Answer 10: $(logx)^{x}\left [ \frac{1}{logx}+log(logx) \right ]+2x^{logx-1}.logx$
Question11$If\: \: f(x)=|cosx|, find\: f'\left ( \frac{3\pi }{4} \right )...Ans.\frac{1}{\sqrt{2}}$
Question 12: $If\: \: y=\sqrt{cosx+\sqrt{cosx+\sqrt{cos+....\infty }}},\: \\prove\: that\: (2y-1)\frac{dy}{dx}=-sinx$Solution 12:$Since\: \: y=\sqrt{cosx+\sqrt{cosx+\sqrt{cos+....\infty }}},$$y=\sqrt{cosx+y}\: \: \Rightarrow \: \: y^{2}=cosx+y$Differentiating both side w. r. t. x we get $2y\frac{dy}{dx}=-sinx+\frac{dy}{dx}$$(2y-1)\frac{dy}{dx}=-sinx$
Question 13. Find dy/dx at x = 1, y = π/4, If Sin2y + cosxy = k
Answer 13.$\frac{\pi (\sqrt{2}+1)}{4}$
Question 14. If x = a(2θ - sin2θ) and y = a(1-cos2θ), find dy/dx, when θ = π/4.
Question 15. Differentiate Log(cosex) w. r. t x ......... Ans[-ex tanx].
Question 16.$If\: y=\sqrt{tanx+\sqrt{tanx+\sqrt{tanx+......\infty }}}$$Prove\: that, (2y-1)\frac{dy}{dx}=Sec^{2}x$
Question 17. $If\: y=\frac{sin^{-1}x}{\sqrt{1-x^{2}}},show\: that:$ $(1-x^{2})\frac{d^{2}y}{dx^{2}}-3x\frac{dy}{dx}-y=0$
Question 18. $If\: x=cost+log\: tan\frac{t}{2},\: y=sint, then$$find\: the\: value\: of\: \: \frac{d^{2}y}{dx^{2}}\: at\: \: t=\frac{\pi }{4}$ $Ans:\: 2\sqrt{2}$
Question 19: Differentiate the following w. r. t. x$y=sin^{-1}\left ( \frac{2^{x+1}}{1+4^{x}} \right )\: .....\: \: Ans:\: \: \frac{2^{x+1}}{1+4^{x}}log\: 2$
Question 20. Differentiate the following w. r. t. x $y=sin^{-1}\left \{ \frac{2^{x+1}.3^{x}}{1+(36)^{x}} \right \}.\: \: ....\: Ans:\: \frac{2(log6)6^{x}}{1+(36)^{x}}$
Question 21. $Differentiate\: y=e^{e^{x}}\: w.\: r.\: t.\: x.\: \: Ans:\: e^{e^{x}}\times e^{x}$
Question 22. Find the value of k if the following function is continuous.$f(x)=\left\{\begin{matrix} \frac{kcosx}{\pi -2x}\; \; ,\; \; x<\frac{\pi }{2}\\\\\frac{3tan2x}{2x-\pi }\; \; ,\; \; x>\frac{\pi }{2} \end{matrix}\right.\; \; \; \; \; \; \; \: \: \: ....\: \: Ans\: \: k=6$
Question 23. Find the value of k for which the following function is continuous at x = 0$f(x)=\left\{\begin{matrix} \frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}\; \; ,\; \; -1\leq x<0\\\\ \frac{2x+1}{x-2}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \:, \: \: \: \: \: \: 0\leq x<1 \end{matrix}\right.\: \: \: \: \: .....\: \: \: \: \: \: Ans\: k=-\frac{1}{2}$
Question 24: Show that f(x) = |x - 2| is continuous but not differentiable at x = 3.
Question 25: Discuss the continuity and differentiability of the following function. $f(x)=\left\{\begin{matrix} 1-x\: \:\: \: \: \: \: \: ,\: \: x<1\\(1-x)(2-x),\: 1\leq x\leq 2 \\ 3-x\: \: \: \: \: ,\: \: \: \: \: x>2 \end{matrix}\right.$
Answer 25: f(x) is continuous at x = 1 but not continuous at x = 2
f(x) is differentiable at x = 1.
As f(x) is not continuous at x = 2 so f(x) is not differentiable at x = 2.

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