Calculus answer check and one question.?

Question

Find the derivative:

1. y=9x^4-5x^2+3x-4
My answer is 36x^3-10x-3

2. y=9x^(-1) - 3x^(-2)+13
Answer: -9x^(-2) +6x ^ (-3)

3. How do I find the derivative for

h(x)= 6/x^6- 5/x^5+ 4 Square root of x?

Thanks

Answer 1

Your first answer was close. It is +3 rather than minus three:

36x^3 - 10x + 3

Your second answer is correct.

h(x) = 6/(x^6) - 5/(x^5) + 4sqrt x

h(x) = 6(x^-6) - 5(x^-5) + 4(x^1/2)

h'(x) = -36(x^-7) + 25(x^-6) + 2(x^-1/2)

Which can also be written as

h'(x) = -36/(x^7) + 25/(x^6) + 2/(sqrt x)

Hope that helps :)

Answer 2

Question 1
y = 9x^4 - 5x² + 3x - 4
dy/dx = 36x³ - 10x + 3

Question 2
y = 9x^(-1) - 3 x^(-2) + 13
dy/dx = - 9 x^(-2) + 6x^(-3)

Question 3
h (x) = 6x^(-6) - 5 x^(-5) + 4 x^(1/2)
h ` (x) = - 36 x^(-7) + 25 x^(-6) + 2 x ^(-1/2)
h `(x) = - 36 /x^7 + 25 / x^6 + 2 /√x

Answer 3

1 and 2 are correct

square root of x = x ^ (1/2)

h(x) = 6/x^6- 5/x^5+ 4 x ^ (1/2)
h'(x) = -36/x^7 + 25/x^6 + 2/x^(1/2)

Answer 4

1. wrong sign

36x^3-10x + 3

2. correct

3. change the question so it is like

6x^(-6) - 5x^(-5) + 4x^(1/2)

like that it can be done the same as the above ones

remember

1/x = x^(-1) and sqrt x = x^(1/2)

Answer 5

1. 9x^4-5x^2+3 (not -3)
2.(-1)9x^(-2) -3 (-2)x^(-3) +0
=-9x^2+6x^(-3) correct
3. 6x^(-6) -5x^(-5) +4x^(1/2)
=6(-6)x^(-7) -5(-5)x^(-6) +4 x^(1/2)
=-36/x^7 +25/x^6 +4(1/2) x^(-1/2)
=-36/x^7 +25/x^6 +2/x^(1/2)

Answer 6

You have 6*x^(-6) - 5*x^(-5) + 4*x^(1/2)

Try working on it from there.