"Find the derivatives of the functions y=1+x−4xx" was answered by students like you

Annette Arroyo

Answered question

2021-10-02

Find the derivatives of the functions

y = 1 + x - 4 \frac{\sqrt{x}}{x}

Answer & Explanation

crocolylec

Skilled2021-10-03Added 100 answers

Step 1
We distribute the denominator and then write using exponents

y = \frac{1 + x - 4 \sqrt{x}}{x}

y = \frac{1}{x} + \frac{x}{x} - \frac{4 \sqrt{x}}{x}

y = x^{- 1} + 1 - 4 x^{- \frac{1}{2}}

Step 2
Then we differentiate both sides using the power rule

y = x^{- 1} + 1 - 4 x^{- \frac{1}{2}}

\frac{d y}{d x} = - 1 x^{- 2} + 0 - 4 (- \frac{1}{2}) x^{- \frac{1}{2} - 1}

\frac{d y}{d x} = - x^{- 2} + 2 x^{- \frac{3}{2}}

\frac{d y}{d x} = - \frac{1}{x^{2}} + \frac{2}{x^{\frac{3}{2}}}

Answer:

\frac{d y}{d x} = - \frac{1}{x^{2}} + \frac{2}{x^{\frac{3}{2}}}

Jeffrey Jordon

Expert2022-11-14Added 2605 answers

Answer is given below (on video)

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