3 x *log(x)
d / 3 \ --\x *log(x)/ dx
Apply the product rule:
f(x)=x3f{\left(x \right)} = x^{3}f(x)=x3; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}dxdf(x):
Apply the power rule: x3x^{3}x3 goes to 3x23 x^{2}3x2
g(x)=log(x)g{\left(x \right)} = \log{\left(x \right)}g(x)=log(x); to find ddxg(x)\frac{d}{d x} g{\left(x \right)}dxdg(x):
The derivative of log(x)\log{\left(x \right)}log(x) is 1x\frac{1}{x}x1.
The result is: 3x2log(x)+x23 x^{2} \log{\left(x \right)} + x^{2}3x2log(x)+x2
Now simplify:
The answer is:
2 2 x + 3*x *log(x)
x*(5 + 6*log(x))
11 + 6*log(x)