Differentiate. $$K ( x ) = \left( 3 x ^ { 5 } + 1 \right) \left( x ^ { 6 } - 4 x \right)$$
A) $15 x ^ { 4 } \left( x ^ { 6 } - 4 x \right) + \left( 3 x ^ { 5 } + 1 \right) \left( 6 x ^ { 5 } - 4 \right)$
B) $\left( x ^ { 6 } - 4 x \right) + \left( 3 x ^ { 5 } + 1 \right)$
C) $15 x ^ { 4 } \left( 6 x ^ { 5 } - 4 \right) + \left( 3 x ^ { 5 } + 1 \right) \left( x ^ { 6 } - 4 x \right)$
D) $15 x ^ { 4 } \left( 6 x ^ { 5 } \right) + \left( 3 x ^ { 5 } \right) \left( x ^ { 6 } - 4 x \right)$
E) $\left( 3 x ^ { 5 } + 1 \right) \left( x ^ { 6 } - 4 x \right) + 15 x ^ { 4 } \left( 6 x ^ { 5 } - 4 \right) + 1$

Question

Quizplus · Accepted Answer

To differentiate using the product rule, we take the derivative of the first term multiplied by the second term, then add that to the derivative of the second term multiplied by the first term. Applying this rule, we get:
$$K'(x) = (3x^5+1)(6x^5-4) + (x^6-4x)(15x^4)$$
Expanding and simplifying, we get:
$$K'(x) = \boxed{15 x ^ { 4 } \left( x ^ { 6 } - 4 x \right) + \left( 3 x ^ { 5 } + 1 \right) \left( 6 x ^ { 5 } - 4 \right)}$$

Differentiate K(x)=(3x5+1)(x6−4x)K ( x ) = \left( 3 x ^ { 5 } + 1 \right) \left( x ^ { 6 } - 4 x \right)K(x)=(3x5+1)(x6−4x)

Differentiate $K ( x ) = \left( 3 x ^ { 5 } + 1 \right) \left( x ^ { 6 } - 4 x \right)$