Differentiate the following functions with respect to x: (cosec x… - Vidyadip

Question

Differentiate the following functions with respect to x:
$\log(\text{cosec x}-\cot\text{x})$

✓

Answer

Consider $\text{y}=\log(\text{cosec x}-\cot\text{x})$
Differentiate with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\log\big(\text{cosec x}-\cot\text{x}\big)$
$=\frac{1}{(\text{cosec x}-\cot\text{x})}\times\big(-\text{cosec x}\cot\text{x}+\text{cosec}^2\text{x}\big)$
[Using chain rule]
$=\frac{1}{(\text{cosec x}-\cot\text{x})}\times\big(-\text{cosec x}\cot\text{x}+\text{cosec}^2\text{x}\big)$
$=\frac{\text{cosec x}(\text{cosec x}-\cos\text{x})}{(\text{cosec x}-\cot\text{x})}$
$=\text{cosec x}$
Hence, the solution is, $\frac{\text{d}}{\text{dx}}\big(\log(\text{cosec x}-\cot\text{x})\big)=\text{cosec x}$

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 "4 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

Find the angle of intersection of the curves y² = 4ax and x² = 4by.

A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of A and ₹ 80 on each piece of type ₹ 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?

Differentiate the following functions with respect to x:
$\sin(2\sin^{-1}\text{x})$

Show that the following set of curves intersect orthogonally.
x³ - 3xy² = -2 and 3x²y - y³ = 2

Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_0\frac{1}{1+\sqrt{\tan\text{x}}}\text{ dx}$

Using integration find the area of the triangular region whose sides have equations y = 2x + 1, y = 3x + 1 and x = 4.

Find the equation of tangent to the curve $x = \sin 3_{t}, y = \cos 2_{t}, \text{at, t} = \frac{\pi}{4} $

If $\text{x}=\text{a}(1+\cos\theta),\text{y}=\text{a}(\theta+\sin\theta),$ prove that

Find the area of the figure bounded by the curves y = |x - 1| and y = 3 - |x|.

There are 2 families A and B. There are 4 men, 6 women and 2 children in family A, and 2 men, 2 women and 4 children in family B. The recommended daily amount of calories is 2400 for men, 1900 for women, 1800 for children and 45 grams of proteins for men, 55 grams for women and 33 grams for children. Represent the above information using matrices. Using matrix multiplication, calculate the total requirement of calories and proteins for each of the 2 families. What awareness can you create among people about the balanced diet from this question?