Forming the Equation of a Tangent Line

[TheWeekndLuv]

I can do the equation stuff but I'm having a hard time computing the derivative of the function.

\The equatian is f(x) = (x^1/2(6-10x²))/x

I know I have to find the derivative of the function but how do i compute f(x+h) into that equation?

Does it go into the x^1/2 and x²?

Is it supposed to be ((x+h)^1/2(6-10(x+h)²))/x? Any help towards this question would be greatly appreciated!!

 

[DrPhil]

I can do the equation stuff but I'm having a hard time computing the derivative of the function.

\The equatian is f(x) = (x^1/2(6-10x²))/x

I know I have to find the derivative of the function but how do i compute f(x+h) into that equation?

Does it go into the x^1/2 and x²?...Yes, and also the x in the denominator.

Is it supposed to be ((x+h)^1/2(6-10(x+h)²))/x? Any help towards this question would be greatly appreciated!!

In that form, it too complicated to do the limit to find the derivative. But the expression can be greatly simplified.

x^1/2 /x = 1/x^1/2, and multiplying by both terms in the parentheses -->

\(\displaystyle f(x) = 6\ x^{-1/2} - 10\ x^{3/2}\)

Each term is a power of x. Have you learned the general power-law rule? I you have already proved that rule using the limit method, then you don't have to do it again. If you need more help, show us how far you got.

 

[TheWeekndLuv]

In that form, it too complicated to do the limit to find the derivative. But the expression can be greatly simplified.

x^1/2 /x = 1/x^1/2, and multiplying by both terms in the parentheses -->

\(\displaystyle f(x) = 6\ x^{-1/2} - 10\ x^{3/2}\)

Each term is a power of x. Have you learned the general power-law rule? I you have already proved that rule using the limit method, then you don't have to do it again. If you need more help, show us how far you got.

okay so if i expand it out it is less complicated like it will be (6x^1/2-10x)/x we just learned the rules yesterday, but then am I applying the the quotient rule?

 

[DrPhil]

okay so if i expand it out it is less complicated like it will be (6x^1/2-10x)/x we just learned the rules yesterday, but then am I applying the the quotient rule?

\(\displaystyle f(x) = 6\ x^{-1/2} - 10\ x^{3/2}\)

The rule you need is the power rule (or do the limit procedure on each of the two terms):

\(\displaystyle \displaystyle \frac{d}{dx}x^y = \frac1y\ x^{y-1}\)

The first term is x to the power (-1/2), and the second term is x to the power (3/2). To differentiate, divide by the power and then decrease the power by 1. THIS IS THE SIMPLEST FORM FOR DIFFERENTIATION!! You will learn that the quotient rule is to be avoided if at all possible.

 

[TheWeekndLuv]

\(\displaystyle f(x) = 6\ x^{-1/2} - 10\ x^{3/2}\)

The rule you need is the power rule (or do the limit procedure on each of the two terms):

\(\displaystyle \displaystyle \frac{d}{dx}x^y = \frac1y\ x^{y-1}\)

The first term is x to the power (-1/2), and the second term is x to the power (3/2). To differentiate, divide by the power and then decrease the power by 1. THIS IS THE SIMPLEST FORM FOR DIFFERENTIATION!! You will learn that the quotient rule is to be avoided if at all possible.

HI I am sorry but I have been trying for the past hour and im not getting it. Each time I keep coming up with a different answer .... Can you please do a step by step process please, I'd greatly appreciate it!!!

 

[stapel]

I have been trying for the past hour and im not getting it. Each time I keep coming up with a different answer .... Can you please do a step by step process please

You already have loads of step-by-step solutions in your textbook and in your classnotes. If you're getting different answers every time, then something is wrong in what you're doing. In other words, examples are not the issue. So another example isn't likely to help.

Instead, please post at least one of your efforts, showing all of your steps, so that we can help you find where you're going wrong. Thank you!

 

[DrPhil]

You already have loads of step-by-step solutions in your textbook and in your classnotes. If you're getting different answers every time, then something is wrong in what you're doing. In other words, examples are not the issue. So another example isn't likely to help.

Instead, please post at least one of your efforts, showing all of your steps, so that we can help you find where you're going wrong. Thank you!

Try one term at a time. The more difficult is the one with the negative exponent:

\(\displaystyle \displaystyle f(x) = 6\ x^{-1/2}\)

Can you set up \(\displaystyle f(x+h) - f(x)\)?