Differentiate the following functions with respect to x -e x -sin x -1-log x

We have, d/dx(e^x+sin x/1+log x ) Using quoteint rule, we get =(1+log x)d/dx(e^x+sin x) (e^x+sin x)d/dx(1+log x)/(1+log x)^2 =(1+log x)(e^x+cos x) (e^x+sin x)1/ ...

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Byju's Answer

Standard XII

Mathematics

Quotient Rule of Differentiation

Differentiate...

Question

Differentiate the following functions with respect to x :

$\frac{e^{x} + s i n x}{1 + l o g x}$

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Solution

We have,

$\frac{d}{d x} (\frac{e^{x} + s i n x}{1 + l o g x})$

Using quoteint rule, we get

$= \frac{(1 + l o g x) \frac{d}{d x} (e^{x} + s i n x) - (e^{x} + s i n x) \frac{d}{d x} (1 + l o g x)}{(1 + l o g x)^{2}}$

$= \frac{(1 + l o g x) (e^{x} + c o s x) - (e^{x} + s i n x) \frac{1}{x}}{(1 + l o g x)^{2}} = \frac{x (1 + l o g x) (e^{x} + c o s x) - (e^{x} + s i n x)}{x (1 + l o g x)^{2}}$

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