Find the implicit derivative d/dx(y=x^(4/x))

 Exercise

$\frac{dy}{dx}\left(y=x^{\frac{4}{x}}\right)$

 

Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

$\frac{d}{dx}\left(y\right)=\frac{d}{dx}\left(x^{\frac{4}{x}}\right)$

 

The derivative of the linear function is equal to $1$

$y^{\prime}=\frac{d}{dx}\left(x^{\frac{4}{x}}\right)$

 

The derivative $\frac{d}{dx}\left(x^{\frac{4}{x}}\right)$ results in $4\left(1-\ln\left(x\right)\right)x^{\left(\frac{4}{x}-2\right)}$

$y^{\prime}=4\left(1-\ln\left(x\right)\right)x^{\left(\frac{4}{x}-2\right)}$

$y^{\prime}=4\left(1-\ln\left(x\right)\right)x^{\left(\frac{4}{x}-2\right)}$

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