Differentiate the following w.r.t.x: ,x>0 - Vidyadip

Question

Differentiate the following w.r.t.x: $\frac{\cos\text{x}}{\log\text{x}},\text{x}>0$

✓

Answer

$\text{Let y}=\frac{\cos\text{x}}{\log\text{x}}$
$\therefore\ \frac{\text{dy}}{\text{dx}} =\frac{(\log\text{x}).\frac{\text{d}}{\text{dx}}(\cos\text{x})-\cos\text{x}.\frac{\text{d}}{\text{dx}}(\log\text{x})}{(\log\text{x})^{2}}$
$ =\frac{(\log\text{x}).(-\sin\text{x})-\cos\text{x}\cdot\frac{\text{1}}{\text{x}}}{(\log\text{x})^{2}}=\frac{-\sin\text{x}\log\text{x}-\frac{\cos\text{x}}{\text{x}}}{(\log\text{x}^{2})}$
$=\frac{-\text{x}\sin\text{x}\ \log\text{x}-\cos\text{x}}{\text{x}(\log\text{x})^2}$

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" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A couple has two children, find the probability that both children are males, if it is known that at least one of the children is male.

Find an angle $\theta$
Whose rate of increase twice is twice the rate of decrease of its cosine.

$\int\sin^2\text{bx dx}$

If A is a square matrix, then write the matrix adj (A^T) − (adj A)^T.

Find $\frac{d y}{d x}$, if x = a ($\theta$ + sin $\theta$), y = a (1 – cos $\theta$).

Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$

Let R₀ denote the set of all non-zero real numbers and let A = R₀ × R₀. If '*' is a binary operation on adefined by,
(a, b) * (c, d) = (ac, bd) for all (a, b), (c, d) ∈ A
Find the invertible element in A.

Find the expected number of boys in a family with 8 children, assuming the sex distribution to be equally probable.

The Cartesian equation of a line is $\frac{{x - 5}}{3} = \frac{{y + 4}}{7} = \frac{{z - 6}}{2}$. Write its vector form.

An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?