Final answer to the problem
$y^{\prime}=\frac{y\left(\ln\left(y\right)+3\cos\left(3x\right)\right)}{y-x}$
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Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(y=xln(y)+sin(3x)). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\ln\left(y\right).
Final answer to the problem
$y^{\prime}=\frac{y\left(\ln\left(y\right)+3\cos\left(3x\right)\right)}{y-x}$
