Differentiate the following function with respect to x:x^3e^x - Vidyadip

Question

Differentiate the following function with respect to x:$\text{x}^3\text{e}^\text{x}\cos\text{x}$

✓

Answer

Let $\text{u}=\text{x}^3;\text{v}=\text{e}^\text{x};\text{w}=\cos\text{x}$Then, $\text{u}'=\text{3x}^2;\text{v}'=\text{e}^\text{x};\text{w}'=-\sin\text{x}$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uvw})=\text{u}'\text{vw}+\text{uv}'\text{w}+\text{uv}\text{w}'$
$\frac{\text{d}}{\text{dx}}(\text{x}^3\text{e}^\text{x}\cos\text{x})=\text{3x}^2\text{e}^\text{x}\cos\text{x}+\text{x}^3\text{e}^\text{x}\cos\text{x}+\text{x}^3\text{e}^\text{x}(-\sin\text{x})$
$=\text{x}^2\text{e}^\text{x}(\text{3}\cos\text{x}+\text{x}\cos\text{x}-\text{x}\sin\text{x})$

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 "3 Marks Question" from Derivatives→Derivatives — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the equation of the straight line passing through $(3, -2)$ and making an angle of $60^\circ$ with the positive direction of y-axis.

If $\cot \text{x}(1+\sin\text{x})=4\text{ m}$ and $\cot \text{x}(1-\sin\text{x})=4\text{ n},$prove that $\text{(m}^2-\text{n}^2)^2=\text{mn.}$

Differentiate the following function with respect to x:$(1-2\tan\text{x})(5+4\sin\text{x})$

If $\text{a}\Big(\frac{1}{\text{b}}+\frac{1}{\text{c}}\Big),\ \Big(\frac{1}{\text{c}}+\frac{1}{\text{a}}\Big),\ \text{c}\Big(\frac{1}{\text{a}}+\frac{1}{\text{b}}\Big)$ are in A.P., proved that a, b, c are in A.P.

Find k so that $\lim\limits_{\text{x}\rightarrow2}\text{f(x)}$ may exist, where $\text{f(x)}=\begin{cases}2\text{x}+3, & \text{x}\le 2\\\text{x}+\text{k}, & \text{x} > 2\end{cases}.$

The first term of a G.P. is 1. The sum of the third term and fifth term is $90.$ Find the common ratio of G.P.

Find the $7$th term from the end in the expansion of $\Big(2\text{x}^2-\frac{3}{2\text{x}}\Big)^8$

If sin $\sin\text{x}=\frac{\sqrt{5}}{3}$ and x lies in IInd quadrant, find the values of $\cos\frac{\text{x}}{2},\sin\frac{\text{x}}{2}$ and $\tan\frac{\text{x}}{2}$

The number of terms of an A.P. is even; the sum of odd terms is 24, of the even terms is 30, and the last term exceeds the first by $10\frac{1}{2},$ find the number of terms and the series.

Let A and B are sets. If $A \cap X = B \cap X = \phi $ and $A \cup X = B \cup X$ for some set X. Show that A = B.
[Hints A = A $\cap$ ( A $\cup$ X ) , B = B $\cap$ ( B $\cup$ X ) and use Distributive law ]