Question

differentiate the problem g(x)=4/3x^3

Answer 1

You mean calculate the derivative?
\[g(x)=3\cdot\frac{4}{3}x^{3-1}=4x^2\]

Answer 2

In g(x) I mean,
\[g'(x)\]

Answer 3

Thats not the answer given in the book its -4x^-4 probably the reason im confused

Answer 4

Not, may be you mean differentiate the function,
\[\frac{4}{3x^3}\]

Answer 5

Then the derivative is,
\[\left(\frac{4}{3}x^{-3}\right)'=\frac{4}{3}(-3)x^{-3-1}=-4x^{-4}\]

Answer 6

Thank you so here is another one f(x)= x/7+ 7/x

Answer 7

\[\left(\frac{x}{7}+\frac{7}{x}\right)'=\left(\frac{x}{7}\right)'+\left(\frac{7}{x}\right)'=\frac{1}{7}+(7x^{-1})'=\frac{1}{7}-7x^{-2}=\frac{1}{7}-\frac{7}{x^2}\]

Answer 8

G(x)=1/3Г8x^2

Answer 9

There is a symbol I don't understand, between the 3 and the 8.

Answer 10

Closest could get to a square root

Answer 11

Ok so it is,
\[G(x)=\frac{1}{3\sqrt{8x^2}}\]?

Answer 12

Or it is a cubic root?
\[G(x)=\frac{1}{\sqrt[3]{8x^2}}\]

Answer 13

Sorry cube root

Answer 14

Ok, then
\[G(x)=(8x^2)^{-1/3}\Rightarrow G(x)=\frac{1}{2}x^{-2/3}\Rightarrow \\
\Rightarrow G'(x)=\frac{1}{2}\frac{-2}{3}x^{-2/3-1}=-\frac{1}{3}x^{-5/3}\]

Answer 15

X^3 cubic root x

Answer 16

You mean,
\[x^3\sqrt[3]{x}\]?

Answer 17

Yes

Answer 18

Sorry to be confusing no computer

Answer 19

Ok, then product rule,
\[(x^3\sqrt[3]{x})'=(x^3)'\sqrt[3]{x}+x^3(\sqrt[3]{x})'=3x^2\sqrt[3]x+x^3\frac{1}{3}x^{-2/3}=3x^{7/3}+\frac{1}{3}x^{7/3}=\frac{10}{3}x^{7/3}\]

Answer 20

\[\eqalign{
&\frac{d}{dx}\frac{4x^3}{3}\\
=&\frac{4}{3}\frac{d}{dx}x^3 \\
=&\frac{4}{3}(3x^2) \\
=&4x^2
}\]

Answer 21

Can you explain that one ?

Answer 22

Another way without product rule,
\[x^3\sqrt[3]{x}=x^{10/3}\Rightarrow (x^{10/3})'=\frac{10}{3}x^{10/3-1}=\frac{10}{3}x^{7/3}\]

Answer 23

Remember,
\[x^3\sqrt[3]x=x^3\cdot x^{1/3}=x^{3+1/3}=x^{10/3}\]

Answer 24

Ok makes sense now x^3(3x)^2

Answer 25

Simplifying
\[x^3(3x)^2=x^39x^2=9x^5\Rightarrow(9x^5)'=45x^4\]

Answer 26

Ok sorry been while for me f(q)=3q^2+4q-2over q

Answer 27

?

Answer 28

You mean,
\[\frac{3q^2+4q-2}{q}\]?

Answer 29

Yes

Answer 30

Then simplify first,
\[3q+4-2/q\]Then derive,
\[(3q+4-2/q)'=3+2/q^2\]

Answer 31

X^2+x^3over x ^2