"Find the derivatives of the given functions. H(x)=x2−4x10x+4" solved and explained

College
Calculus and Analysis
Differential Calculus
Derivatives

Isa Trevino

Answered question

2021-10-19

Find the derivatives of the given functions.

H (x) = \frac{x^{2} - 4 x}{10 x + 4}

Answer & Explanation

grbavit

Skilled2021-10-20Added 109 answers

Step 1
We will need the quotient rule. For that assume u and v and find u' and v'
$H (x) = \frac{x^{2} - 4 x}{10 x + 4}$
$u = x^{2} - 4 x$
$u^{'} = 2 x - 4$
$v = 10 x + 4$
$v^{'} = 10$
Step 2
Plug them in the quotient rule and simplify.
H'(x)
$= \frac{u^{'} v - u v^{'}}{v^{2}}$
$= \frac{(2 x - 4) (10 x + 4) - (x^{2} - 4 x) (10)}{{(10 x + 4)}^{2}}$
$= \frac{20 x^{2} + 8 x - 40 x - 16 - 10 x^{2} + 40 x}{{(10 x + 4)}^{2}}$
$= \frac{10 x^{2} + 8 x - 16}{{(10 x + 4)}^{2}}$
Answer: $\frac{10 x^{2} + 8 x - 16}{{(10 x + 4)}^{2}}$

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