If y=(tan x)^{sin x},then frac{dy}{dx} is equ | vedclass

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

Question

(A) Given $y = (	an x)^{\sin x}$.Taking the natural logarithm on both sides,we get $\log y = \sin x \log(	an x)$.Differentiating both sides with res

Vedclass · Accepted Answer

$(	an x)^{\sin x}\{\sec x+(\cos x)(\log (	an x))\}$

Vedclass · Answer

(A) Given $y = (	an x)^{\sin x}$.Taking the natural logarithm on both sides,we get $\log y = \sin x \log(	an x)$.Differentiating both sides with respect to $x$ using the product rule:$\frac{1}{y} \frac{dy}{dx} = \cos x \log(	an x) + \sin x \cdot \frac{1}{	an x} \cdot \sec^2 x$.Since $\frac{\sin x}{	an x} = \cos x$,the expression simplifies to:$\frac{1}{y} \frac{dy}{dx} = \cos x \log(	an x) + \cos x \cdot \sec^2 x$.Note that $\cos x \cdot \sec^2 x = \cos x \cdot \frac{1}{\cos^2 x} = \sec x$.Therefore,$\frac{dy}{dx} = y \{\sec x + \cos x \log(	an x)\}$.Substituting $y = (	an x)^{\sin x}$,we get $\frac{dy}{dx} = (	an x)^{\sin x} \{\sec x + \cos x \log(	an x)\}$.

If $y=(\tan x)^{\sin x}$,then $\frac{dy}{dx}$ is equal to

Similar Questions

Differentiate the function with respect to $x$: $(x+3)^{2} \cdot(x+4)^{3} \cdot(x+5)^{4}$

If $y = (\tan x)^{\cot x}$,then $\frac{dy}{dx} =$

If $x^{m} y^{n}=(x+y)^{m+n}$,then $\frac{dy}{dx}$ is equal to

If $y(\cos x)^{\sin x}=(\sin x)^{\sin x}$, then the value of $\frac{dy}{dx}$ at $x=\frac{\pi}{4}$ is

If $y = \frac{x^2}{(x - 1)(x - 2)(x - 3)} + \frac{2x}{(x - 2)(x - 3)} + \frac{3}{x - 3} + 1$,then $\frac{xy'}{y}$ is equal to (where $y' = \frac{dy}{dx}$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module