multiple choice 1 point\nwhat is the derivative of \\( \\frac { 4 x ^ { 5 } - 5 x ^ { 2 } } { x } \\)?\n\\(…

multiple choice 1 point\nwhat is the derivative of \\( \\frac { 4 x ^ { 5 } - 5 x ^ { 2 } } { x } \\)?\n\\( \\frac { 20 x ^ { 4 } - 10 x } { \\ln ( x ) } \\)\n\\( 16 x ^ { 3 } - 5 \\)\n\\( ( 20 x ^ { 4 } - 10 x ) \\cdot \\ln ( x ) \\)\n\\( 20 x ^ { 3 } - 10 x \\)\n\\( 4 x ^ { 4 } - 5 x \\)\nclear my selection

multiple choice 1 point\nwhat is the derivative of \\( \\frac { 4 x ^ { 5 } - 5 x ^ { 2 } } { x } \\)?\n\\( \\frac { 20 x ^ { 4 } - 10 x } { \\ln ( x ) } \\)\n\\( 16 x ^ { 3 } - 5 \\)\n\\( ( 20 x ^ { 4 } - 10 x ) \\cdot \\ln ( x ) \\)\n\\( 20 x ^ { 3 } - 10 x \\)\n\\( 4 x ^ { 4 } - 5 x \\)\nclear my selection

Answer

Explanation:

Step1: Simplify the function

Divide each term in the numerator by (x): [ \begin{align*} \frac{4x^{5}-5x^{2}}{x}&=\frac{4x^{5}}{x}-\frac{5x^{2}}{x}\ & = 4x^{4}-5x \end{align*} ]

Step2: Apply the power rule

The power rule for differentiation is (\frac{d}{dx}(x^{n})=nx^{n - 1}). For (y = 4x^{4}-5x), the derivative of (4x^{4}) is (4\times4x^{4-1}=16x^{3}), and the derivative of (-5x) is (-5\times1x^{1 - 1}=- 5).

Answer:

(16x^{3}-5)