Differentiate the Following Functions from First Principles Eax+B. - Mathematics

प्रश्न

Differentiate the following functions from first principles e^ax^+b.

उत्तर

$Let f (x) = e^{a x + b}$
$\Rightarrow f (x + h) = e^{a (x + h) + b}$
$∴ \frac{d}{d x} (f (x)) = lim_{h \to 0} \frac{f (x + h) - f (x)}{h}$
$= lim_{h \to 0} \frac{e^{a (x + h) + b} - e^{(a x + b)}}{h}$
$= lim_{h \to 0} \frac{e^{a x + b} e^{a h} - e^{a x + b}}{h}$
$= lim_{h \to 0} e^{a x + b} {\frac{(e^{a h} - 1)}{a h}} \times a$
$= a e^{a x + b} lim_{h \to 0} {\frac{(e^{a h} - 1)}{a h}}$
$= a e^{a x + b}$
$S o, \frac{d}{d x} (e^{a x + b}) = a e^{a x + b}$

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Simple Problems on Applications of Derivatives

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अध्याय 11: Differentiation - Exercise 11.01 [पृष्ठ १७]

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अध्याय 11 Differentiation
Exercise 11.01 | Q 3 | पृष्ठ १७

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Differentiate the Following Functions from First Principles Eax+B. - Mathematics

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