Derivative of a rational function

MathematicsDerivativesEasyYKS

Published: June 8, 2026

Question

$$f(x) = \frac{x^3 + 2x}{x^2}$$ $$f'(x) = ?$$

Animated Video Solution

The first half plays free, the full solution is in the app.

Step 1

Merhaba! Bugun verilen rasyonel fonksiyonun turevini alacagiz. Fonksiyonumuz f x esittir x kup arti iki x bolu x karedir.

f(x) = \frac{x^3 + 2x}{x^2}

Step 2

Turev almadan once ifadeyi sadelestirmek islemimizi oldukca kolaylastiracaktir. Paydaki her terimi paydadaki x kareye bolelim.

Step 3

Simdi bu kesirleri sadelestirelim. x kup bolu x kare, x eder. iki x bolu x kare ise iki bolu x, yani iki carpi x ustu eksi bir eder.

Step 4

Artik fonksiyonun turevini almak icin temel turev kurallarini uygulayabiliriz.

f'(x) = \frac{d}{dx}(x + 2x^{-1})

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