Question

Find the derivative of each function defined as follows: y=5x^-5-6x^-2+13x^-1

Answer 1

You are just differentiating x with respect to y?

Answer 2

Do you know how the power rule works in derivatives?

Answer 3

derivative of x^(-n) is -n*x^(-n-1)

Answer 4

Hi! yes, I know how the power rule works

Answer 5

Look at what matricked did.

Answer 6

so derivative of 5x^-5 = -5*5x^-6 = -25 x^-6
and similar for the rest..

Answer 7

\[5x ^{-5}=-5x ^{-5-1}=-5x ^{-6}\]

Answer 8

That's just for the first term, but the others are done the same way.

Answer 9

Ok, let me try it out. Thanks!

Answer 10

My answer is: \[25x ^{-6}+12x^{-3}+13x ^{-2}\]

Answer 11

Use the power rule and the signal rule:\[y=x^k\\y'=kx^{k-1}\]_______________________________________________________________
\[y=5x^{-5}-6x^{-2}+13x^{-1}\]\[y'=5*(-5)*x^{-5-1}-6*(-2)*x^{-2-1}+13*(-1)*x^{-1-1}\]\[y'=-25x^{-6}+12x^{-3}-13x^{-2}\]

Answer 12

Do I have to do anything about the negative exponents? or can this be my final answer?

Answer 13

You forgot the signal rule, if the exponents is negative, you should multiple the rest by the negative exponent, for example:\[y=4x^{-3}\]The derivative will be (pay attention in the exponent\[y'=4*(-3)*x^{-3-1}\]the answer will be\[y'=-12*x^{-4}\]The second derivative will be\[y''=-12*(-4)*x^{-4-1}\]\[y''=48*x^{-5}\]

Answer 14

Ok, thank you!

Answer 15

You're welcome ;)