Use Logarithmic Differentiation to Find the Derivative

The use of logarithms to streamline a function before determining its derivative is essentially what logarithmic differentiation is. It proves to be exceedingly beneficial when handling functions that incorporate exponents or multiplications of variables. This method necessitates applying the natural log to both equation sides, simplifying them, and subsequently differentiating, all by adhering to the standard logarithmic rules.

The problems about Use Logarithmic Differentiation to Find the Derivative

Topic	Problem	Solution
None	Let $f (x) = x^{7 x}$ . Use logarithmic differentiati…	Let $f (x) = x^{7 x}$ . We want to find the derivative of this function.
None	Differentiate and simplify: $y=\sqrt[5]{(\ln x)^{…	Given the function $y = \sqrt[5]{(\ln x)^{4}}$
None	Find the derivative of $y$ with respect to $x$ . \…	Given the function $y = \log_{2} ({(\frac{x + 7}{x - 7})}^{\ln 2})$
None	Suppose $u$ and $v$ are functions of $x$ , and $f(…	Suppose $u$ and $v$ are functions of $x$ , and $f (x) = \ln (u v) + u^{2}$ . If $u(1)=2, v(1)=7, u^{\prime…