Find the derivative of x^ -4 (3-4 x^ -5 ) - Vidyadip

Question

Find the derivative of $x^{-4}\left(3-4 x^{-5}\right)$

✓

Answer

Here $f(x)=x^{-4}\left(3-4 x^{-5}\right)$
$f^{\prime}(x)=\frac{d}{d x}\left[x^{-4}\left(3-4 x^{-5}\right)\right]$
$=x^{-4} \frac{d}{d x}\left(3-4 x^{-5}\right)+\left(3-4 x^{-5}\right) \frac{d}{d x}\left(x^{-4}\right)$
$\begin{array}{l}=x^{-4}\left(20 x^{-6}\right)+\left(3-4 x^{-5}\right)\left(-4 x^{-5}\right) \\ =20 x^{-10}-12 x^{-5}+16 x^{-10} \\ =36 x^{-10}-12 x^{-5}=\frac{36}{x^{10}}-\frac{12}{x^5}\end{array}$

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 Model Paper 10→Model Paper 10 — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Solve the following system of equations in R.
$\frac{2\text{x}-3}{4}-2\geq\frac{4\text{x}}{3}-6,2(2\text{x}+3)<6(\text{x}-2)+10$

In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?

A company manufactures cassettes and its cost and revenue functions for a week are $\text{C}=300+\frac{3}{2}\text{x}$ R = 2x respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?

Prove that: $^{4\text{n}}\text{C}_{2\text{n}}:^{2\text{n}}\text{C}_{\text{n}}=[1,3,5...(4\text{n}-1):[1,3,5...(2\text{n-1})^{2}].$

18 mice were placed in two experimental groups and one control group, with all groups equally large. In how many ways can the mice be placed into three groups?

How many different words can be formed with the letters of word 'SUNDAY'? How many of the words begin with N? How many begin with N and end in Y?

The vertices of $\Delta PQR$, are P(2, 1), Q(-2, 3) and R (4, 5). Find equation of the median through the vertex R.

$1+\text{i}^2+\text{i}^4+\text{i}^6+\text{i}^8+ ...+\text{i}^{20}$

Which term of the G.P.:

$\sqrt{3},3,3\sqrt{3},\ \dots\text{is}729?$

The longest side of a triangle is twice the shortest side and the third side is 2cm longer than the shortest side. If the perimeter of the triangle is more than 166cm then find the minimum length of the shortest side.