# Math Help - differentiation

1. ## differentiation

not sure how todo differentiations
can any one explain how to do this equasion

y=3x^4 -3√x+8

2. Originally Posted by bart 1000
not sure how todo differentiations
can any one explain how to do this equasion

y=3x^4 -3√x+8
$y = 3x^4 - 3x^{1/2} + 8$

$\frac{dy}{dx} = 12x^3 - 1.5x^{-1/2}$

3. Originally Posted by bart 1000
not sure how todo differentiations
can any one explain how to do this equasion

y=3x^4 -3√x+8
First lets quote the power rule

$\frac{d}{dx}x^n=nx^{n-1}$

Now lets rewrite y with fractional exponents using

$\sqrt[b]{x^a}=x^{\frac{a}{b}}$

So

$y=3x^4-3x^{\frac{1}{2}}+8$

Just use the power rule

4. thanks for your help, i understand how to get 12x^3 but getting a bit lost on
what happens to -3√x+8 ??????

5. Originally Posted by bart 1000
thanks for your help, i understand how to get 12x^3 but getting a bit lost on
what happens to -3√x+8 ??????
√x = x^0.5

So, lower the power by 1 to make it -1/2, then multiply the co-efficient by 1/2 to make it -1.5

6. Originally Posted by bart 1000
thanks for your help, i understand how to get 12x^3 but getting a bit lost on
what happens to -3√x+8 ??????

Do you mean?

$\sqrt{x+8}=(x+8)^{\frac{1}{2}}$

If so

$\frac{d}{dx}(x+8)^{\frac{1}{2}}=\frac{1}{2}(x+8)^{-\frac{1}{2}}=\frac{1}{2\sqrt{x+8}}$