The differential coefficient of f(sin x) with | vedclass

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

Question

(B) Given that $f(x) = \log x.$We need to find the derivative of $f(\sin x)$ with respect to $x.$Let $y = f(\sin x) = \log(\sin x).$Using the chain ru

Vedclass · Accepted Answer

$\cot x$

Vedclass · Answer

(B) Given that $f(x) = \log x.$We need to find the derivative of $f(\sin x)$ with respect to $x.$Let $y = f(\sin x) = \log(\sin x).$Using the chain rule,we differentiate with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx}[\log(\sin x)]$$\frac{dy}{dx} = \frac{1}{\sin x} \cdot \frac{d}{dx}(\sin x)$$\frac{dy}{dx} = \frac{1}{\sin x} \cdot \cos x$$\frac{dy}{dx} = \cot x.$Therefore,the correct option is $B$.

The differential coefficient of $f(\sin x)$ with respect to $x,$ where $f(x) = \log x,$ is

Similar Questions

If $f(x) = 2x^2 + 3x - 5$,then the value of $f'(0) + 3f'(-1)$ is equal to

Find the derivative of the following function with respect to $x$ (where $p, q, r, s$ are fixed non-zero constants): $(p x+q)\left(\frac{r}{x}+s\right)$.

If $y = \sin^{98}(x) \cdot \cos^{39}(x)$,then find $\frac{dy}{dx}$.

Find the derivative: $\frac{d}{dx}[\cos((1 - x^2)^2)] = ?$

The derivative of ${x^6} + {6^x}$ with respect to $x$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module