How do I find the first derivative of a function using the power rule?

[raeshun]

f(x)=x^2-3x-3x^-2+5x^-3

I need help finding the 1st derivative of this function using the power rule.If you can help can you explain how you got the answer.I tried like five times but the differentiation calculator says I am getting the wrong answer.heres how o attempted it.

f(x)'=(2)(x)^2-1 - (3)(x)^1-1 - (3)(-2)(x)^-2-1 + (-3)(5)(x)^-3-1

here i am applying the power rule to each variable, coefficient and exponent group they each have a different color to help you identify them with the original function.

f(x)'=2x-3+6x^-3 -15x^-4
and this is the answer i get

this is the answer i should get

f(x)'=(2x^5-3x^4+6x-15)/(x^4)

 

[Sourabh N]

f(x)=x^2-3x-3x^-2+5x^-3

I need help finding the 1st derivative of this function using the power rule.If you can help can you explain how you got the answer.I tried like five times but the differentiation calculator says I am getting the wrong answer.heres how o attempted it.

f(x)'=(2)(x)^2-1 - (3)(-2)(x)^1-1 - (3)(x)^-2-1 + (-3)(5)(x)^-3-1

ooo colors!
Notice the edit (in boldface) I have made. Do you see where you went wrong?

 

[raeshun]

ooo colors!
Notice the edit (in boldface) I have made. Do you see where you went wrong?

i fixed it.the coefficients are right but the exponents don't match up.

 

[Sourabh N]

They do match for me. Can you show what you're getting? (and how you obtain it)

 

[HallsofIvy]

The two answers are exactly the same. Just do the indicated division.

 

[e^(i Pi)+1=0]

You'll find this more and more in calculus. Your answer and the answer key may look different but still be equivalent.

 

[raeshun]

The two answers are exactly the same. Just do the indicated division.

You'll find this more and more in calculus. Your answer and the answer key may look different but still be equivalent.

I'm sorry i am new to differentiation but how to i do the division?

 

[Mark44]

You don't actually have to do any division. Multiply the numerator by x⁴ and multiply the denominator by x⁴. In other words, you're multiplying your answer by 1, to get rid of the negative exponents in the numerator.

 

[raeshun]

You don't actually have to do any division. Multiply the numerator by x⁴ and multiply the denominator by x⁴. In other words, you're multiplying your answer by 1, to get rid of the negative exponents in the numerator.

It worked thanks :).but why do you multiply by x^4 instead of X^3 or something like that?

 

[SammyS]

It worked thanks :).but why do you multiply by x^4 instead of X^3 or something like that?

... because you have an x^-4 in you expression for the derivative.

 

[Sourabh N]

It worked thanks :).but why do you multiply by x^4 instead of X^3 or something like that?

... because you have an x^-4 in you expression for the derivative.

Also because there is an x⁴ in the denominator in the answer. ;)

 

[Mark44]

It worked thanks :).but why do you multiply by x^4 instead of X^3 or something like that?

... because you have an x^-4 in you expression for the derivative.

Also because there is an x⁴ in the denominator in the answer. ;)

The only reason for multiplying by x⁴ over itself is because of the x^-4 term in the numerator. The x⁴ is a result of this multiplication, not the reason for it.