Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . You need not expand your answer. ? $y = \left( 9 x ^ { 2 } + x \right) \left( x - x ^ { 2 } \right)$
A) $( 18 x + 1 ) ( 1 - x ) + \left( x - x ^ { 2 } \right) \left( 9 x ^ { 2 } + x \right)$
B) $( 18 x + 1 ) \left( x - x ^ { 2 } \right) + ( 1 - 2 x ) \left( 9 x ^ { 2 } - x \right)$
C) $( 18 x + 1 ) \left( x - x ^ { 2 } \right) + ( 1 - 2 x ) \left( 9 x ^ { 2 } + x \right)$
D) $- 36 x ^ { 2 } + 20 x + 1$
E) $( 18 x + 1 ) ( 1 - x ) + \left( x - 2 x ^ { 2 } \right) \left( 9 x ^ { 2 } + x \right)$

Question

Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . You need not expand your answer. ? $y = \left( 9 x ^ { 2 } + x \right) \left( x - x ^ { 2 } \right)$ 
A) $( 18 x + 1 ) ( 1 - x ) + \left( x - x ^ { 2 } \right) \left( 9 x ^ { 2 } + x \right)$
B) $( 18 x + 1 ) \left( x - x ^ { 2 } \right) + ( 1 - 2 x ) \left( 9 x ^ { 2 } - x \right)$
C) $( 18 x + 1 ) \left( x - x ^ { 2 } \right) + ( 1 - 2 x ) \left( 9 x ^ { 2 } + x \right)$
D) $- 36 x ^ { 2 } + 20 x + 1$
E) $( 18 x + 1 ) ( 1 - x ) + \left( x - 2 x ^ { 2 } \right) \left( 9 x ^ { 2 } + x \right)$

Quizplus · Accepted Answer

To find the derivative of $y = (9x^2 + x)(x - x^2)$, we use the product rule: $\frac{d}{dx}[u \cdot v] = u'v + uv'$. Let $u = 9x^2 + x$ and $v = x - x^2$. Then, $u' = 18x + 1$ and $v' = 1 - 2x$. Applying the product rule, we get $(18x + 1)(x - x^2) + (1 - 2x)(9x^2 + x)$, which matches choice C.

Calculate dy dx\frac { \mathrm { d } y } { \mathrm {~d} x } dxdy​

Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$