Share

Books Shortlist

# Solution for If Y = X Tan X + √ X 2 + 1 2 , Find D Y D X ? - CBSE (Commerce) Class 12 - Mathematics

ConceptSimple Problems on Applications of Derivatives

#### Question

$\text{ If }y = x^{\tan x} + \sqrt{\frac{x^2 + 1}{2}}, \text{ find} \frac{dy}{dx}$ ?

#### Solution

$y = x^{\tan x } + \sqrt{\frac{x^2 + 1}{2}}$
$\text{ Taking log on both sides, we get }$
$\log y = \tan x\log x + \frac{1}{2}\log\left( \frac{x^2 + 1}{2} \right)$
$\Rightarrow \frac{1}{y}\frac{dy}{dx} = \frac{\tan x}{x} + \sec^2 x\log x + \frac{1}{2} \times \frac{2}{x^2 + 1} \times x$
$\Rightarrow \frac{1}{y}\frac{dy}{dx} = \frac{\tan x}{x} + \sec^2 x\log x + \frac{x}{x^2 + 1}$
$\Rightarrow \frac{dy}{dx} = \left( x^{\tan x } + \sqrt{\frac{x^2 + 1}{2}} \right)\left( \frac{\tan x}{x} + \sec^2 x\log x + \frac{x}{x^2 + 1} \right)$
$\Rightarrow \frac{dy}{dx} = x^{\tan x } \left( \frac{\tan x}{x} + \sec^2 x\log x \right) + \frac{x}{\sqrt{2 x^2 + 2}}$

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [1]

Solution If Y = X Tan X + √ X 2 + 1 2 , Find D Y D X ? Concept: Simple Problems on Applications of Derivatives.
S