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Differentiate the following functions with respect to $x:\; sinx(ax+b)$

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Toolbox:
  • According to the Chain Rule for differentiation, given two functions $f(x)$ and $g(x)$, and $y=f(g(x)) \rightarrow y' = f'(g(x)).g'(x)$.
  • $\; \large \frac{d(sinx)}{dx} $$= cosx$
Given $y = sinx(ax+b)$:
According to the Chain Rule for differentiation, given two functions $f(x)$ and $g(x)$, and $y=f(g(x)) \rightarrow y' = f'(g(x)).g'(x)$
$\; \large \frac{d(sinx)}{dx} $$= cosx$
$\Rightarrow$ Given $g(x) = ax+b \rightarrow g'(x) = a$
$\Rightarrow f'(g(x)) = f'(sin(ax+b) = cos(ax+b)$
$\Rightarrow $ $y' = f'(g(x)).g'(x) = cos(ax+b).a = a.cos(ax+b)$
answered Apr 4, 2013 by balaji.thirumalai
 
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