4 x *log(x)
d / 4 \ --\x *log(x)/ dx
Apply the product rule:
f(x)=x4f{\left(x \right)} = x^{4}f(x)=x4; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}dxdf(x):
Apply the power rule: x4x^{4}x4 goes to 4x34 x^{3}4x3
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: 4x3log(x)+x34 x^{3} \log{\left(x \right)} + x^{3}4x3log(x)+x3
Now simplify:
The answer is:
3 3 x + 4*x *log(x)
2 x *(7 + 12*log(x))
2*x*(13 + 12*log(x))