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Question Number 171667 by Mastermind last updated on 19/Jun/22

Answered by mindispower last updated on 19/Jun/22

$$ln\left(y\right)=ln\left(x\right)ln\left(cos\left(x\right)\right)+\frac{1}{2}ln(x^2-5x+3{log}_4\left(x\right))$$$$\frac{y^{\prime }}{y}=\frac{1}{x}ln\left(cos\left(x\right)\right)-tg\left(x\right)ln\left(x\right)+\frac{2x-5+\frac{3}{xln\left(4\right)}}{2(x^2-5x+3{log}_4\left(x\right))}$$$$y^{\prime }={\left(cos\left(x\right)\right)}^{ln\left(x\right)}\sqrt{x^2-5x+3{log}_4\left(x\right)}(\frac{ln\left(cos\left(x\right)\right)}{x}-tg\left(x\right)\frac{ln\left(x\right)}{x}+\frac{2x-5x+\frac{3}{xln\left(4\right)}}{2(x^2-5x+3{log}_4\left(x\right)})$$

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