If y= (x+9) , then dy dx at x = 0 is: - Vidyadip

MCQ

If $\text{y}=\frac{\sin(\text{x}+9)}{\cos\text{x}},$ then $\frac{\text{dy}}{\text{dx}}$ at $x = 0$ is:

✓
$\cos9$
B
$\sin9$
C
$0$
D
$1$

✓

Answer

Correct option: A.

$\cos9$

$\text{y}=\frac{\sin(\text{x}+9)}{\cos\text{x}}$
Differentiate both the sides with respect to $x,$ we get
$\frac{\text{dy}}{\text{dx}}=\frac{(\cos\text{x})\frac{\text{d}}{\text{dx}}\sin(\text{x}+9)-\sin(\text{x}+9)\frac{\text{d}}{\text{dx}}(\cos\text{x})}{\cos^2\text{x}} ($Quotient rule$)$
$=\frac{(\cos\text{x})(\cos(\text{x}+9))-(\sin(\text{x}+9))(-\sin\text{x})}{\cos^2\text{x}}$
$=\frac{(\cos\text{x})(\cos(\text{x}+9))+(\sin(\text{x}+9))(\sin\text{x})}{\cos^2\text{x}}$
$=\frac{\cos(\text{x}+9-\text{x})}{\cos^2\text{x}}$
$=\frac{\cos9}{\cos^2\text{x}}$
Thus, $\frac{\text{dy}}{\text{dx}}$ at $x = 0$ is $\cos9$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Limits and Derivatives→Limits and Derivatives — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If the $1011^{\text {th }}$ term from the end in the binomial expansion of $\left(\frac{4 x}{5}-\frac{5}{2 x }\right)^{2022}$ is 1024 times $1011^{\text {th }}$ term from the beginning, then $|x|$ is equal to

If ‘$a$’ and ‘$c$’ are the segments of a focal chord of a parabola and b the semi-latus rectum, then

The points $(-5, 12), (-2, -3), (9, -10), (6, 5)$ taken in order, form:

The values of parameter $'a'$ such that the line $\left( {{{\log }_2}\left( {1 + 5a - {a^2}} \right)} \right)x - 5y - \left( {{a^2} - 5} \right) = 0$ is a normal to the curve $xy = 1$ , may lie in the interval

The equations of the tangents drawn from the origin to the circle ${x^2} + {y^2} - 2rx - 2hy + {h^2} = 0$ are

Let $f(x) = \frac{{x\,\,.\,\,{2^x}\,\, - \,\,x}}{{1\,\, - \,\,\cos \,x}} \& g(x) = 2^x sin \left( {\frac{{\ell n\,2}}{{{2^x}}}} \right)$ then :

$R({z^2}) = 1$ is represented by

In an election the number of candidates is $1$ greater than the persons to be elected. If a voter can vote in $254$ ways, then the number of candidates is

For $n \in Z$ , the general solution of the equation

$(\sqrt 3 - 1)\,\sin \,\theta \, + \,(\sqrt 3 + 1)\,\cos \theta \, = \,2$ is

The range of the function $f(x) = P$ is: