What is the derivative of the function f(x)=\frac{3x-5}{5x+2}?

Layla-Rose Ellison

Layla-Rose Ellison

Answered question

2022-02-28

What is the derivative of the function
f(x)=3x55x+2?

Answer & Explanation

Jenson Mcculloch

Jenson Mcculloch

Beginner2022-03-01Added 9 answers

Step 1
The quotient rule states that
if y=f(x)g(x), then dydx=f(x)g(x)g(x)f(x)(g(x))2
Now if we apply this to the given function
f(x)=3(5x+2)5(3x5)(5x+2)2
f(x)=15x+615x+25(5x+2)2
f(x)=31(5x+2)2
twaza7fl

twaza7fl

Beginner2022-03-02Added 5 answers

Step 1
Quotient Rule: (uv)=vuuvv2
(uv)=(5x+2)(3)(3x5)(5)(5x+2)2
=15x+6(15x25)(5x+2)2
=31(5x+2)2
If you are enrolled in a calculus course, you really need to review these elementary differentiation rules.

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