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Solved Examples
Solution:
Given y= 3x2 + 9x + 6
$\frac{dy}{dx}$ = 3$\frac{d}{dx}(x^{2})$ + 9$\frac{d}{dx}(x)$ + $\frac{d}{dx}(6)$
= 3(2x) + 9
= 6x + 9
Solution:
Given y = $3^{x}$ + $e^{x}(x^{2})$
$\frac{dy}{dx}$ = $\frac{d}{dx}(3^{x})$ + $\frac{d}{dx}(e^{x} . x^{2})$
= $3^{x}$ + $x^{2}\frac{d}{dx}(e^{x})$ + $e^{x}\frac{d}{dx}(x^{2})$
= $3^{x}$ + $x^{2} e^{x}$ + 2x $e^{x}$
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Solved Example
Solution:
Given y = x log x
$\frac{dy}{dx}$ = x $\frac{d}{dx}(\log x)$ + $\log x \frac{d}{dx}(x)$
= x $\times\frac{1}{x}$ + $\log x (1)$
= 1 + $\log x$