If y = x sin x,then | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the function $y = x \sin x$. Taking the natural logarithm on both sides: $\ln y = \ln(x \sin x)$. Using the property $\ln(ab) = \ln a + \ln

Vedclass · Accepted Answer

$\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \cot x$

Vedclass · Answer

(A) Given the function $y = x \sin x$. Taking the natural logarithm on both sides: $\ln y = \ln(x \sin x)$. Using the property $\ln(ab) = \ln a + \ln b$,we get $\ln y = \ln x + \ln(\sin x)$. Differentiating both sides with respect to $x$: $\frac{d}{dx}(\ln y) = \frac{d}{dx}(\ln x) + \frac{d}{dx}(\ln(\sin x))$. Applying the chain rule: $\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{1}{\sin x} \cdot \cos x$. Simplifying the expression: $\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \cot x$.

If $y = x \sin x$,then

Similar Questions

$\frac{d}{dx}\left( \frac{1}{x^4 \sec x} \right) = $

If $y = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + .....\infty$,then $\frac{dy}{dx} = $

$\int \frac{dx}{{(2ax - x^2)}^{1/2}} = a^n \sin^{-1} \left( \frac{x}{a} - 1 \right)$. In this formula,$n =$ . . . . . . .

$\int\limits_0^{\frac{\pi }{4}} {\sin 2x} \,dx$ is equal to

The value of $\cos\, 120^{\circ}$ is .....

Vedclass Test Series

Exam Paper Generator

Online Exam Module