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 "5 Marks Questions" 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 distance of the point (-1, -5, -10) from the point of intersection of the line $\vec{\text{r}}=2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}+\lambda\Big(3\hat{\text{i}}+4\hat{\text{j}}+2\hat{\text{k}}\Big)$ and the plane $\vec{\text{r}}.\Big(\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}\Big)=5.$

Find the shortest distance between the lines whose vector equations are $ \vec r = \left( {1 - t} \right)\hat i + (t - 2)\hat j + (3 - 2t)\hat k$ and $\vec r = \left( {s + 1} \right)\hat i + (2s - 1)\hat j - (2s + 1)\hat k$

Solve the following differential equation:
$\text{cosec }x\ \log\text{ y}\frac{\text{dy}}{\text{d}x}+x^2\text{y}^2=0$

Find the values of a and b if the slope of the tangent to the curve xy + ax + by = 2 at (1, 1) is 2.

Evaluate the following integrals:$\int\frac{(\text{x}-1)^2}{\text{x}^2+2\text{x}+2}\text{ dx}$

Using integration, find the area of the region: $\left\{(\text{x},\text{y}) : |\text{x}-1|<\text{y}<\sqrt{5-\text{x}^{2}}\right\}$.

Find the area of the ragion bounded by $x^2 = 4$ay and its latusrectum.

If the line $\frac{\text{x}-3}{2}=\frac{\text{y}+2}{-1}=\frac{\text{z}+4}{3}$ lies in the plane $lx + my - z = 9$, then find the value of $l^2 + m^2.$

Draw a rough sketch of the region $\{(x, y) : y^2 < 3x, 3x^2 + < 16\}$ and find the area by the region using mwthod of integration.

Calculate the area of the ragion bounded by $y^2= x$ and $x^2= y$.