Find the derivative of function a x^4 - b x^2 + x (it is to be un… - Vidyadip

Question

Find the derivative of function $\frac{a}{{{x^4}}} - \frac{b}{{{x^2}}} + \cos x$ (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers).

✓

Answer

Here $f(x) = \frac{a}{{{x^4}}} - \frac{b}{{{x^2}}} + \cos x = a{x^-4} - b{x^{ - 2}} + \cos x$
$\therefore \;f{\text{'}}(x) = \frac{d}{{dx}}[a{x^{ - 4}} - b{x^2} + \cos x]$$= a\frac{d}{{dx}}({x^{ - 4}}) - b\frac{d}{{dx}}({x^{ - 2}}) + \frac{d}{{dx}}(\cos x)$
$ - a{x^{ - 5}} + 2b{x^{ - 3}} - \sin x = \frac{{ - 4a}}{{{x^5}}} + \frac{{2b}}{{{x^3}}} - \sin x$
$- 4a{x^{ - 5}} + 2b{x^{ - 3}} - \sin x = \frac{{ - 4a}}{{{x^5}}} + \frac{{2b}}{{{x^3}}} - \sin x$

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 Limits and Derivatives→Limits and Derivatives — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Prove that $4\text{A}=4\sin\text{A}\cos^3\text{A}-4\cos\text{A}\sin^3\text{A}.$

In a simultanepous throw of a pair of dice, find the probability of getting,

A number greather than 4 on each die.

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that at least one will be green?

If $\Big(\frac{1+\text{i}}{1-\text{i}}\Big)^3-\Big(\frac{1-\text{i}}{1+\text{i}}\Big)^3=\text{x}+\text{iy},$ then find (x, y).

What are the odds in favour of getting a spade if a card is drawn from a well - shuffled deck of cards? what are the odds in favour of getting a king?

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow\frac{-\pi}{2^+}}\sec\text{x}$

Is $A =\{ x : x \in N , 1< x \leq 2\}$ null set?

Solve x² + x + 1= 0

Find what the following equations become when the origin is shifted to the point (1, 1)?
x² + y² − x + 2y = 0