Use the rules for derivatives to find the derivatives below. y=x−x2; use the Power Rule

f(x)=y1=x−x2we have to find the derivative by using the power rule:Power Rule:ddx(x)n=n(x)n−1Nowy1=x12−x2f′(x)=y1′=12x12−1−2x2−1=12x−12−2x=12x−2xHence, f′(x)=y1′=12x−2x

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Answered question

2021-10-01

Use the rules for derivatives to find the derivatives below.

y = \sqrt{x} - x^{2}

; use the Power Rule

Answer & Explanation

Ayesha Gomez

Skilled2021-10-02Added 104 answers

f (x) = y_{1} = \sqrt{x} - x^{2}

we have to find the derivative by using the power rule:
Power Rule:

\frac{d}{d x} {(x)}^{n} = n {(x)}^{n - 1}

Now

y_{1} = x^{\frac{1}{2}} - x^{2}

f^{'} (x) = y_{1}^{'} = \frac{1}{2} x^{\frac{1}{2} - 1} - 2 x^{2 - 1}

= \frac{1}{2} x^{- \frac{1}{2}} - 2 x

= \frac{1}{2 \sqrt{x}} - 2 x

Hence,

f^{'} (x) = y_{1}^{'} = \frac{1}{2 \sqrt{x}} - 2 x

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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