Differentiate the following function with respect to x:x^5(3-6x^ … - Vidyadip

Question

Differentiate the following function with respect to x:$\text{x}^5(3-\text{6x}^{-9})$

✓

Answer

Let $\text{u}=\text{x}^5;\text{v}=(3-\text{6x}^{-9})$Then, $\text{u}'=\text{5x}^4;\text{v}'=\text{54x}^{-10}$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}[\text{x}^5(3-\text{6x}^9)]=\text{x}^5(\text{54x}^{-10})+\text{5x}^4(3-\text{6x}^9)$
$=\text{54x}^{-5}+\text{15x}^4-\text{30x}^{-5}$
$=\text{15x}^4+\text{24x}^{-5}$

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

If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt{2},$ then obtain the equation of the hyperbola.

If $\tan\theta_1\tan\theta_2=\text{k},$ then $\frac{\cos(\theta_1-\theta_2)}{\cos(\theta_1+\theta_2)}=$

Find the equation of a parabola with vertex at the origin, the axis along x-axis and passing through (2, 3).

The means and standard deviations of heights ans weights of 50 students of a class are as follows:

	Weights	Heights
Mean	63.2kg	63.2 inch
Standard deviation	5.6kg	11.5 inch

Which shows more variability, heights or weights?

Find the derivative of function $2 \tan x - 7 \sec x$

Find the sum of the following arithmetic progression:
$\frac{\text{x}-\text{y}}{\text{x}+\text{y}},\ \frac{3\text{x}-2\text{y}}{\text{x}+\text{y}},\ \frac{5\text{x}-3\text{y}}{\text{x}+\text{y}},\ ...$ to n terms.

An arc is in the form of a semi-ellipse. It is $8$ m wide and $2$ m high at the centre. Find the height of the arch at a point $1.5$ m from one end.

Solve the following linear inequations in R:
$\frac{\text{x}-1}{\text{x}+3}>2$

The function f is defined by $\text{f(x)}=\begin{cases}\text{x}^2,& 0\leq\text{x}\leq3\\3\text{x},&3\leq\text{x}\leq10\end{cases}$
The relation g is defined by $\text{g(x)}=\begin{cases}\text{x}^2,& 0\leq\text{x}\leq2\\3\text{x},&2\leq\text{x}\leq10\end{cases}$
Show that f is a function and g is not a function.

A man deposited ₹ $10,000$ in a bank at the rate of $5\%$ simple interest annually. Find the amount in $15^{th} $ year since he deposited the amount and also calculate the total amount after $20$ year.