Question

Differentiate: $f\left(x\right)={\left[\log \left(7x+3\right)\right]}^5$ with respect to $x$.

Answer 1

$\begin{array}{c}f\left(x\right)={\left[\log \left(7x+3\right)\right]}^5\\ \left\{\begin{array}{c}usingformulas\\ f\left(x\right)=x^n\Rightarrow f^{\prime }\left(x\right)=n{x}^{n-1}\\ g\left(x\right)=\log x\Rightarrow g^{\prime }\left(x\right)=\frac{1}{x}\end{array}\right\}\\ f^{\prime }\left(x\right)=5{\left[\log \left(7x+3\right)\right]}^4\times \frac{1}{\left(7x+3\right)}\times 7\\ =35\frac{{\left[\log \left(7x+3\right)\right]}^4}{\left(7x+3\right)}\end{array}$