Find the derivative of the function: frac{d}{ | vedclass

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

Question

(B) Let $y = (\sin x)^{\log x}$.Taking the natural logarithm on both sides:$\log y = \log x \cdot \log \sin x$.Differentiating both sides with respect

Vedclass · Accepted Answer

$(\sin x)^{\log x} \left[ \frac{1}{x} \log \sin x + \cot x \log x \right]$

Vedclass · Answer

(B) Let $y = (\sin x)^{\log x}$.Taking the natural logarithm on both sides:$\log y = \log x \cdot \log \sin x$.Differentiating both sides with respect to $x$ using the product rule:$\frac{1}{y} \frac{dy}{dx} = \frac{d}{dx}(\log x) \cdot \log \sin x + \log x \cdot \frac{d}{dx}(\log \sin x)$.$\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} \log \sin x + \log x \cdot \frac{1}{\sin x} \cdot \cos x$.$\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} \log \sin x + \cot x \log x$.Therefore,$\frac{dy}{dx} = y \left[ \frac{1}{x} \log \sin x + \cot x \log x \right]$.Substituting $y = (\sin x)^{\log x}$:$\frac{dy}{dx} = (\sin x)^{\log x} \left[ \frac{1}{x} \log \sin x + \cot x \log x \right]$.

Find the derivative of the function: $\frac{d}{dx} \{(\sin x)^{\log x}\}$

Similar Questions

Find the derivative: $\frac{d}{dx}(x^{\log_e x})$

If $y=x^{\log x}+(\log x)^x, x>1$ then $\left(\frac{d y}{d x}\right)_{x=e}=$

$\frac{d}{dx}\{(\sin x)^x\} = $

If $y = \frac{e^{2x} \cos x}{x \sin x}$,then $\frac{dy}{dx} = $

If $f(x)=(1+x)(1+x^2)(1+x^4)(1+x^8)$,then $f^{\prime}(1)=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module