Differentiate.
-$x ^ { 3 }$ ln x
A) 3 $x ^ { 2 }$ ln x + $x ^ { 2 }$
B) ( $3 x ^ { 2 }$ + 1) ln x
C) 3 $x ^ { 2 }$ ln x
D) $x ^ { 2 }$ ln x + $x ^ { 2 }$
E) none of these

Question

Differentiate. 
-$x ^ { 3 }$ ln x
A) 3 $x ^ { 2 }$ ln x + $x ^ { 2 }$
B) ( $3 x ^ { 2 }$ + 1) ln x
C) 3 $x ^ { 2 }$ ln x
D) $x ^ { 2 }$ ln x + $x ^ { 2 }$
E) none of these

Quizplus · Accepted Answer

This differentiation requires the product rule, which is $d(uv)/dx = u(dv/dx) + v(du/dx)$ where $u = x^3$ and $v = \ln(x)$. Differentiating $u$ gives $3x^2$ and differentiating $v$ gives $1/x$. Substituting these into the product rule formula gives $3x^2 \ln(x) + x^2$.

Differentiate x3x ^ { 3 }x3 Ln X A) 3 x2x ^ { 2 }x2

Differentiate $x ^ { 3 }$ Ln X
A) 3 $x ^ { 2 }$