find the derivative of y = 1/3x -4

Question

I dont understand the concept

Answer 1

First, I'd like to give you a little advice. Finding a derivative is a fundamental topic in calculus. I would recommend you finding a tutor here on this site. 

 

But to answer your question, to find the derivative, the standard analytical process is

 

If f(x)=nx^m 

 

then the derivative is

 

f’(x)=mnx^m-1

 

For your equation

n=1/3

m=1

 

So the derivative is

f’(x)=1(1/3)x⁰=1(1/3)(1)=1/3

 

Because 4 is a constant, it's derivative with respect to x is 0.

 

So the full derivative is simply

f’(x)=1/3

 

Please let me know if this isn't clear. And, again, I recommend find a  tutor on Wyzant.

Answer 2

f(x)=3x/(x^2-16)

f(x)=3x/(x-4)(x+4)

vertical asymptotes

x-4=0

x=4 is a vertical asymptote

x+4=0

x=-4 is a vertical asymptote

 

horizontal asymptotes

when the numerator has degree less than the denominator, the horizontal asymptote is y=0 because the function approaches 0 because the denominator gets larger and larger and therefore the function gets smaller and smaller

(numerator has degree 1 and denominator has degree 2)

Answer 3

Derivative means slope of the tangent, which will vary according to what x is, unless you have a straight line, which has a constant slope. A shortcut to find the derivative, is to use the Power Rule: for each term take the exponent of x, multiply it by the coefficient of x, put it in front and then reduce the exponent of x by exactly 1.

 

So 1/3x (I assume this is 1/3 * x for now) becomes 1/3*1*x⁰ = 1/3

-4 has an unwritten x⁰  , so the derivative = 0

 

ANSWER = 1/3

 

If it was 1/(3x), I'll let you prove that the derivative = -1/(3x²). You start by rewriting as 1/3*x^-1