Differentiate the following function with respect to x:x^5e^x+x^6 - Vidyadip

Question

Differentiate the following function with respect to x:$\text{x}^5\text{e}^\text{x}+\text{x}^6\log\text{x}$

✓

Answer

$\frac{\text{d}}{\text{dx}}=(\text{x}^5\text{e}^\text{x}+\text{x}^6\log\text{x})$$=\text{x}^5\frac{\text{d}}{\text{dx}}(\text{e}^\text{x})+\text{e}^\text{x}\frac{\text{d}}{\text{dx}}(\text{x}^5)+(\text{x})^6\frac{\text{d}}{\text{dx}}(\log\text{x})+\log\text{x}\frac{\text{d}}{\text{dx}}(\text{x}^6)$
$=\text{x}^5\text{e}^\text{x}+\text{e}^\text{x}(5\text{x}^4)+\text{x}^6.\frac{1}{\text{x}}+\log\text{x}(6\text{x}^5)$
$=\text{x}^5\text{e}^\text{x}+\text{e}^\text{x}(5\text{x}^4)+\text{x}^5+\log\text{x}(6\text{x}^5)$
$=\text{x}^4(\text{x}\text{e}^\text{x}+5\text{e}^\text{x}+\text{x}+\text{6x}+\log\text{x})$

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 "2 Marks Questions" 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

In how many ways can $6$ boys and $5$ girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?

If a double ordinate of the parabola $y^2=4 a x$ be of length $8 a$, then prove that the angle between the lines joining the vertex of the parabola to the ends of this double ordinate is right angle.

Prove that:
$\cos^2(\frac{\pi}{4}-\text{x})-\sin^2(\frac{\pi}{4}-\text{x})=\sin2\text{x}$

Solve the following linear inequations in $R:$
Solve: $-4x > 30,$ when

$\text{x}\in\text{R}$
$\text{x}\in\text{Z}$
$\text{x}\in\text{N}$

Find the most general value of $\theta$ satisfying the equation $\tan\theta=-1$ and $\cos\theta=\frac{1}{\sqrt{2}}.$

Find the derivative of $(x^3 - 27)$ from first principle.

The numbers $1, 2, 3$ and $4$ are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement.
Describe the following events:
$A =$ The number on the first slip is larger than the one on the second slip.
$B =$ The number on the second slip is greater than $2.$
$C =$ The sum of the numbers on the two slips is $6$ or $7$.
$D =$ The number on the second slips is twice that on the first slip.
Which pair$(s)$ of events is $($are$)$ mutually exclusive?

Which term in the expansion of $\Bigg\{\Big(\frac{\text{x}}{\sqrt{\text{y}}}\Big)^\frac{1}{3}+\bigg(\frac{\text{y}}{\text{x}^\frac{1}{3}}\bigg)^\frac{1}{2}\Bigg\}^{21}$ contains x and y to one and the same power?

If $\left(\frac{1+i}{1-i}\right)^{m} = 1$ then find the least positive integral value of $m.$

Find x in the following.
$\frac{1}{4!}+\frac{1}{5!}=\frac{\text{x}}{6!}$