Mathematics, 27.01.2020 22:31 cheesy7651
Use logarithmic differentiation to find the derivative of the following equation. y = (6x + 1)5(x4 − 5)6
Answers: 3
![\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{\frac{dy}{dx}}{y}=5\cdot \cfrac{6}{6x+1}+6\cdot \cfrac{4x^3}{x^4-5} \\\\\\ \cfrac{\frac{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]](/tpl/images/0473/6923/728a0.png)
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Use logarithmic differentiation to find the derivative of the following equation. y = (6x + 1)5(x4 −...
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