Question

Use logarithmic differentiation to find the derivative of the following equation. y = (6x + 1)5(x4 − 5)6

Answer 1

as far as I can tell


`\bf y=(6x+1)^5(x^4-5)^6\implies ln(y)=ln[\ (6x+1)^5(x^4-5)^6\ ] \\\\\\ ln(y)=ln[(6x+1)^5]+ln[(x^4-5)^6] \\\\\\ ln(y)=5ln[(6x+1)]+6ln[(x^4-5)] \\\\\\ \cfrac{(dy)/(dx)}{y}=5\cdot \cfrac{6}{6x+1}+6\cdot \cfrac{4x^3}{x^4-5} \\\\\\ \cfrac{(dy)/(dx)}{y}=\cfrac{30}{6x+1}+\cfrac{24x^3}{x^4-5} \\\\\\ \cfrac{dy}{dx}=y\left[ \cfrac{30}{6x+1}+\cfrac{24x^3}{x^4-5} \right]`