"Find the derivatives without using product or quotient..." solved and explained

College
Calculus and Analysis
Differential Calculus
Derivatives

Josh Sizemore

Answered question

2021-12-10

Find the derivatives without using product or quotient rules.

f (x) = (\frac{2}{x^{\frac{1}{3}}}) + 3 \cos x

Answer & Explanation

Dabanka4v

Beginner2021-12-11Added 36 answers

Step 1
Calculation:
Compute the derivative of the given function as follows.
$f^{'} (x) = \frac{d}{d x} (\frac{2}{x^{\frac{1}{3}}} + 3 \cos x)$
$= \frac{d}{d x} (2 x^{\frac{- 1}{3}}) + \frac{d}{d x} (3 \cos x) [∵ S u m r u l e o f d e r i v a t i v e]$
Step 2
Apply power rule of derivative and simplify it.
$f^{'} (x) = \frac{- 2 x^{\frac{- 4}{3}}}{3} - 3 \sin x [∵ \frac{d}{d x} (\cos x) = - \sin x]$
$= \frac{- 2}{3 x^{\frac{4}{3}}} - 3 \sin x$
Step 3
Thus, the derivative of the given function is $(- \frac{2}{3} x^{\frac{4}{3}}) - 3 \sin x$ .

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