Question

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

Explanation:

Step1: Simplify the function

Divide each term in the numerator by \(x\):

$$
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$$

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:

\(16x^{3}-5\)