If $y=\{f(x)\}^{\phi(x)}$, then $\frac{d y}{d x}$ is

$\frac{\phi}{f}\left(\frac{d f}{d x}\right)+\frac{d \phi}{d x} \log f$

$e^{\phi \log f}\left\{\phi \frac{f^{\prime}}{f}+\phi^{\prime} \log f^{\prime}\right\}$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

y=\{f(x)\}^{\phi(x)}

, then

\frac{d y}{d x}

View answer and explanation

Correct option: A

f^{\phi \log f}\left\{\frac{\phi}{f} \frac{d f}{d x}+\log f \cdot \frac{d \phi}{d x}\right\}

Option A (

f^{\phi \log f}\left{\frac{{\phi}}{{f}} \frac{{d f}}{{d x}}+\log f \cdot \frac{{d \phi}}{{d x}}\right\}

) is correct because it is the result of applying logarithmic differentiation to the function

y = \{f(x)\} ^{\phi(x)}

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