Practicing Success
Practicing Success
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If $y=\{f(x)\}^{\phi(x)}$, then $\frac{d y}{d x}$ is |
$e^{\phi \log f}\left\{\frac{\phi}{f} \frac{d f}{d x}+\log f . \frac{d \phi}{d x}\right\}$ $\frac{\phi}{f}\left(\frac{d f}{d x}\right)+\frac{d \phi}{d x} \log f$ $e^{\phi \log f}\left\{\phi \frac{f'}{f}+\phi' \log f'\right\}$ none of these |
$e^{\phi \log f}\left\{\frac{\phi}{f} \frac{d f}{d x}+\log f . \frac{d \phi}{d x}\right\}$ |
We have, $y=\{f(x)\}^{\phi(x)}=e^{\phi(x) \log f(x)}$ $\Rightarrow \frac{d y}{d x}=e^{\phi(x) \log f(x)}\left\{\phi'(x) \log f(x)+\frac{\phi(x)}{f(x)} f'(x)\right\}$ |
