CBSE 11th Standard Maths Subject Limits and Derivatives Ncert Exemplar 1 Marks Questions 2021
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CBSE 11th Standard Maths Subject Limits and Derivatives Ncert Exemplar 1 Marks Questions 2021
11th Standard CBSE
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Reg.No. :
Mathematics
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Find the derivative of 2x4 + x
(a)8x3+1
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Find the derivative of the following functions.
\(\frac { 3x+4 }{ 5x^{ 2 }-7x+9 } \)(a)\(y=\frac { 3x+4 }{ 5{ x }^{ 2 }-7x+9 }\)
\( \frac { dy }{ dx } =\frac { (5{ x }^{ 2 }-7x+9)\frac { d }{ dx } (3x+4)-(3x+4)\frac { d }{ dx } (5{ x }^{ 2 }-7x+9) }{ (5{ x }^{ 2 }-7x+9)^{ 2 } } \)
Ans: \(\frac { 55-15x^{ 2 }-40x }{ (5{ x }^{ 2 }-7x+9)^{ 2 } } \) -
Find the derivative of the following functions.
cosecx cotx(a)-cosec3x-cot2x cosecx
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Find the derivative of the following functions.
(secx-1)(secx+1)(a)(secx-1)(secx+1)=sec2x-1=tan2x
=tan x. tan x
Ans. 2tan x sec2 x -
Find the derivative of the following functions.
(ax2+cotx)(p+qcosx)(a)Let y = (ax2 + cot x) (p + q cosx).
Then, \(\frac { dy }{ dx } =\left( { ax }^{ 2 }+cotx \right) \frac { d }{ dx } (p+qcosx)+(p+qcosx)\frac { d }{ dx } ({ ax }^{ 2 }+cotx)\)
\(=-qsinx({ ax }^{ 2 }+cotx)+(p+qcosx)(2ax-{ cosec }^{ 2 }x)\)
1 Marks
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CBSE 11th Standard Maths Subject Limits and Derivatives Ncert Exemplar 1 Marks Questions 2021 Answer Keys
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8x3+1
8x3+1
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\(y=\frac{3 x+4}{5 x^2-7 x+9}\)
\(\frac{d y}{d x}=\frac{\left(5 x^2-7 x+9\right) \frac{d}{d x}(3 x+4)-(3 x+4) \frac{d}{d x}\left(5 x^2-7 x+9\right)}{\left(5 x^2-7 x+9\right)^2}\)
Ans: \(\frac{55-15 x^2-40 x}{\left(5 x^2-7 x+9\right)^2}\)\(y=\frac{3 x+4}{5 x^2-7 x+9}\)
\(\frac{d y}{d x}=\frac{\left(5 x^2-7 x+9\right) \frac{d}{d x}(3 x+4)-(3 x+4) \frac{d}{d x}\left(5 x^2-7 x+9\right)}{\left(5 x^2-7 x+9\right)^2}\)
Ans: \(\frac{55-15 x^2-40 x}{\left(5 x^2-7 x+9\right)^2}\) -
-cosec3x-cot2x cosecx
-cosec3x-cot2x cosecx
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(secx-1)(secx+1)=sec2x-1=tan2x
=tan x. tan x
Ans. 2tan x sec2 x(secx-1)(secx+1)=sec2x-1=tan2x
=tan x. tan x
Ans. 2tan x sec2 x -
Let y = (ax2 + cot x) (p + q cosx).
Then, \(\frac{d y}{d x}=\left(a x^2+\cot x\right) \frac{d}{d x}(p+q \cos x)+(p+q \cos x) \frac{d}{d x}\left(a x^2+\cot x\right)\)
\(=-q \sin x\left(a x^2+\cot x\right)+(p+q \cos x)\left(2 a x-\operatorname{cosec}^2 x\right)\)Let y = (ax2 + cot x) (p + q cosx).
Then, \(\frac{d y}{d x}=\left(a x^2+\cot x\right) \frac{d}{d x}(p+q \cos x)+(p+q \cos x) \frac{d}{d x}\left(a x^2+\cot x\right)\)
\(=-q \sin x\left(a x^2+\cot x\right)+(p+q \cos x)\left(2 a x-\operatorname{cosec}^2 x\right)\)
1 Marks
