Expert Answer to "Find the derivatives of the functions g(x)=x2−4x+0.5" - Plainmath

petrusrexcs

Answered question

2021-12-06

Find the derivatives of the functions

g (x) = x^{2} - \frac{4}{x} + 0.5

Answer & Explanation

Maricela Alarcon

Beginner2021-12-07Added 28 answers

Step 1
Given:

g (x) = \frac{x^{2} - 4}{x + 0.5}

Step 2
Differentiate with respect to 'x':

g^{'} (x) = \frac{d}{d x} (\frac{x^{2} - 4}{x + 0.5})

Apply the Quotient Rule:

{(\frac{f}{g})}^{'} = \frac{f^{'} \cdot g - f \cdot g^{'}}{g^{2}}

Here,

f = x^{2} - 0.4

, g=x+0.5

g^{'} (x) = \frac{\frac{d}{d x} (x^{2} - 4) (x + 0.5) - \frac{d}{d x} (x + 0.5) (x^{2} - 4)}{{(x + 0.5)}^{2}}

g^{'} (x) = \frac{2 x (x + 0.5) - 1 (x^{2} - 4)}{{(x + 0.5)}^{2}}

g^{'} (x) = \frac{2 x^{2} + x - x^{2} + 4}{{(x + 0.5)}^{2}}

g^{'} (x) = \frac{x^{2} + x + 4}{{(x + 0.5)}^{2}}

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