Differentiate the following functions with respect to x: x+ - Vidyadip

Question

Differentiate the following functions with respect to x:$\frac{\text{x}+\cos\text{x}}{\tan\text{x}}$

✓

Answer

We have,$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{x}+\cos\text{x}}{\tan\text{x}}\Big)$
Using quotient rule, we get
$\frac{(\tan\text{x})\frac{\text{d}}{\text{dx}}(\text{x}+\cos\text{x})-(\text{x}+\cos\text{x})\frac{\text{d}}{\text{dx}}(\tan\text{x})}{(\tan^2\text{x})}$
$=\frac{\tan\text{x}\Big\{1+(-\sin\text{x})\Big\}-(\text{x}+\cos\text{x})\sec^2\text{x}}{(\tan^2\text{x})}$
$=\frac{(1-\sin\text{x})\tan\text{x}-(\text{x}+\cos\text{x})\sec^2\text{x}}{(\tan^2\text{x})}$

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 "(Each question 4 marks)" from Derivatives→Derivatives — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Sketch the graphs of the following curves on the same scale and the same axes: $\text{y}=\cos2\text{x}$ and $\text{y}=\cos2\Big(\text{x}-\frac{\pi}{4}\Big)$

Find the multiplicative inverse of the following complex numbers: $(1-\text{i}\sqrt{3})^2$

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas: $4(y - 1)^2 = -7(x - 3)$.

Find the equation of the ellips whose focus is in the following case:focus is (1, 2), directricx is 3x + 4y - 5 = 0 and $\text{e}=\frac{1}{2}.$

Find the eccentricity, coordinates of the foci, equations of directrices and lenght of the latus-rectum of the hyperbola $2\text{x}^{2}-3\text{y}^{2}=5.$

Represent to solution set of each of the following inequations graphically in two dimensional plane: $0\leq2\text{x}-5\text{y}+10$

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:
The number of people who read at least one of the newspapers.

show that the solution set of the following system of linear inequalities is an unbounded region $2\text{x}+\text{y}\geq8,\text{x}+2\text{y}\geq10,\text{x}\geq0,\text{y}\geq0.$

Find the equation of the circle which passes through the origin and cuts off chords of lengths $4$ and $6$ on the positive side of the x-axis and y-axis respectively.

Prove that the area of the parallelogram formed by the lines 3x - 4y + a = 0, 3x - 4y + 3a= 0, 4x - 3y - a = 0 and 4x - 3y - 2a = 0 is $\frac{2\text{a}^2}{7}$ sq.units.