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.
| 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 \(y=\log _{2}\left(\left(\frac{x+7}{x-7}\right)^{\ln 2}\right)\) |
| 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… |