Differentiate the following equation-e x log- x tan x

D/dx(e^x log √(x) tan x) Apply product rule, = log √(x)× tan x d/dx (e^x) +e^x× tan x d/dx (log √(x)) +e^x log √(x)d/dx(tan x) = log √(x)× tan e^x +e^x tan x 1/ ...

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Byju's Answer

Standard XII

Mathematics

Product Rule of Differentiation

Differentiate...

Question

Differentiate the following equation:
$e^{x} l o g \sqrt{x} t a n x$

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Solution

$\frac{d}{d x} (e^{x} l o g \sqrt{x} t a n x)$
Apply product rule,
$= l o g \sqrt{x} \times t a n x \frac{d}{d x} (e^{x}) + e^{x} \times t a n x \frac{d}{d x} (l o g \sqrt{x}) + e^{x} l o g \sqrt{x} \frac{d}{d x} (t a n x)$
$= l o g \sqrt{x} \times t a n e^{x} + e^{x} t a n x \frac{1}{2 x} + e^{x} l o g \sqrt{x} \times s e c^{2} x$
$= \frac{1}{2} l o g x \times t a n x \times e^{x} + \frac{1 t a n x}{2 x} e^{x} \frac{1}{2}$
$l o g x s e c^{2} x$ $[∵ l o g \sqrt{x} = \frac{1}{2} l o g x]$
$= \frac{1}{2} e^{x} (l o g x \times t a n x + \frac{t a n x}{x} + l o g x s e c^{2} x)$

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Differentiate the following equation: exlog √x tan x

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Differentiate the following equation:
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