Apply the product rule:
dxdf(x)g(x)h(x)=f(x)g(x)dxdh(x)+f(x)h(x)dxdg(x)+g(x)h(x)dxdf(x)
f(x)=x3; to find dxdf(x):
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Apply the power rule: x3 goes to 3x2
g(x)=sin(x); to find dxdg(x):
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The derivative of sine is cosine:
dxdsin(x)=cos(x)
h(x)=log(x); to find dxdh(x):
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The derivative of log(x) is x1.
The result is: x3log(x)cos(x)+3x2log(x)sin(x)+x2sin(x)