Question
Find the derivative of $x^5 (3 - 6x^{-9})$
✓
Answer
Here $f(x) = x^5 (3 - 6x^{-9})$
$ = {x^5}\frac{d}{{dx}}(3 - 6{x^{ - 9}}) + (3 - 6{x^{ - 9}})\frac{d}{{dx}}({x^5})$
$= x^5(54x^{-10}) + (3 - 6x^{-9}) \times 5x^4$
$= 54x^{-5} + 15x^4 - 30x^{-5}$
$= 24x^{-5} + 15x^4$
$= \frac{{24}}{{{x^5}}} + 15{x^4}$
$ = {x^5}\frac{d}{{dx}}(3 - 6{x^{ - 9}}) + (3 - 6{x^{ - 9}})\frac{d}{{dx}}({x^5})$
$= x^5(54x^{-10}) + (3 - 6x^{-9}) \times 5x^4$
$= 54x^{-5} + 15x^4 - 30x^{-5}$
$= 24x^{-5} + 15x^4$
$= \frac{{24}}{{{x^5}}} + 15{x^4}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Write the number of points of intersection of the curves $2\text{y}=-1$ and $\text{y = cosec x}.$
→Evaluate: $\frac{{n!}}{{(n - r)!}}$ when, n = 6, r = 2
→Write down the negation of following compound statement:
All rational numbers are real and complex.
All rational numbers are real and complex.
Rewrite the following statements in the form of conditional statement:
The unit digit of an integer is 0 or 5 if it is divisible by 5.
The unit digit of an integer is 0 or 5 if it is divisible by 5.
What is the formula to find the $n$th term of G.P. from the end?
→Given an example of a statement P(n) such that it is true for all $\text{n}\in\text{N}.$
→Identify the quantifier in the following statements and write the negation of the statements.
There exists a capital for every state in India.
There exists a capital for every state in India.
Which of the following sentences are statements? Justify.
A triangle has three sides.
A triangle has three sides.
Negate the following statements:
There exists a number which is equal to its square.
There exists a number which is equal to its square.
The figure shows a relationship between the sets P and Q. Write this relation roster form. What is its domain and range?
