Download App

Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives1 Mark
MCQ
What is the value of $\frac{\text{d}}{\text{dx}}\text{(ex sinx + ex cos ⁡x)}?$
  • A
    $0$
  • B
    $\text{2 cos⁡x}$
  • C
    $2e^x.\sin ⁡x$
  • ✓
    $2e^x.\cos⁡ x$
✓

Answer

Correct option: D.
$2e^x.\cos⁡ x$
We need to use product rule in both the terms to get the answer.
$=\frac{d}{dx}(\text{f.g})=\text{g}\frac{d}{dx}(\text{f})+\text{f}\frac{d}{dx}(\text{fg})$
$=\frac{\text{d}}{\text{dx}} (\text{e}^{\text{x}} \sin \text{x} + \text{e}^{\text{x}} \cos \text{⁡x}) = ({\text{e}^{\text{x}},.\frac{\text{d}}{\text{dx}}} (\sin⁡\text{x}) + \text{sin ⁡x}.\frac{\text{d}}{\text{dx}} (\text{e}^{\text{x}})) + (\text{e}^{\text{x}}.\frac{\text{d}}{\text{dx}} (\cos \text{⁡x}) + \cos⁡ \text{x}.\frac{\text{d}}{\text{dx}} (\text{e}^{\text{x}}))$
$=\frac{\text{d}}{\text{dx}} (\text{e}^{\text{x}} \sin \text{x} + \text{e}^{\text{x}} \cos \text{⁡x}) =(\text{e}^{\text{x}}.\cos⁡ \text{x} + \sin \text{⁡x} . \text{e}^{\text{x}}) + (\text{e}^{\text{x}}.(-\sin ⁡\text{x}) + \cos ⁡\text{x}.\text{e}^{\text{x}})$
$= \frac{\text{d}}{\text{dx}} (\text{e}^{\text {x}} \sin \text{x} + \text{e}^{\text {x}} \cos \text{⁡x}) = \text{e}^{\text {x}}.\cos⁡ \text{x} + \sin⁡ \text{x} . \text{e}^{\text {x}} – \text{ex}.\sin⁡ \text{x} + \cos \text{⁡x}.\text{e}^{\text {x}}$
$= \frac{\text{d}}{\text{dx}} (\text{e}^{\text{x}} \sin \text{x} + \text{e}^{\text{x}} \cos \text{x}) = 2\text{e}^{\text{x}}.\text{cos}⁡ \text{x}$

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 one end of a focal chord $\mathrm{AB}$ of the parabola $\mathrm{y}^{2}=8 \mathrm{x}$ is at $\mathrm{A}\left(\frac{1}{2},-2\right),$ then the equation of the tangent to it at $\mathrm{B}$ is 
→
If $\alpha$ and $\beta$ are acute angles satisfying $\cos2\alpha=\frac{3\cos2\beta-1}{3-\cos2\beta},$ then $\tan\alpha=$
→
Consider a family of circles which are passing through the point $(- 1, 1)$ and are tangent to $x-$ axis. If $(h, k)$ are the coordinate of the centre of the circles, then the set of values of $k$ is given by the interval
→
$\tan 75^\circ - \cot 75^\circ = $
→
The value of $\cos^\text{2}48^\circ-\sin^\text{2}48^\circ$ is:
→
The length of perpendicular drawn from origin $(0,0)$ to line $x \sec \theta+y \operatorname{cosec} \theta=a$ is given by :
→
If $(a + ib)(c + id)(e + if)(g + ih)$$ = A + iB,$ then $({a^2} + {b^2})({c^2} + {d^2})({e^2} + {f^2})({g^2} + {h^2})$ =
→
Choose the correct answer.Given the integers $r > 1, n > 2,$ and coefficients of $(3r)^{th}$ and $(r + 2)^{nd}$ terms in the binomial expansion of $(1 + x)^{2n}$ are equal, then:
→
Sentence involving variable time such as today, tomorrow, or yesterday are.
→
The points $\left( {\frac{a}{{\sqrt 3 }},a} \right),\;\left( {\frac{{2a}}{{\sqrt 3 }},\,2a} \right),\;\left( {\frac{a}{{\sqrt 3 }},\,3a} \right)$ are the vertices of
→