Question

Can someone differentiate 1/4x^2 (Show step by step) please? Thank you .

Answer 1

Is your question this \[\frac {d}{dx} \left[ \frac {1}{4x^2} \right]\]or this?\[\frac {d}{dx} \left[ \frac {1}{4} x^2 \right]\]

Answer 2

the first one.

Answer 3

You can rewrite that 1/(4x^2) with a negative exponent because one of the laws of exponents is\[\frac {1}{x^n} = x^{-n}\]So what you have is\[\frac {d}{dx} \left[ \frac {1}{4x^2} \right] = \frac {d}{dx} \left[ \frac {1}{4}x^{-2} \right]\]Now you can apply the power rule.\[\frac {d}{dx} \left[ x^n \right] = nx^{n-1}\]\[\frac {d}{dx} \left[ \frac {1}{4}x^{-2} \right] = \frac {-2}{4} x^{-3} = \frac {-1}{2x^3}\]Done.

Answer 4

There is a second method, using the quotient rule. Would you like to see it?

Answer 5

Sure. However, I thought you add 1 when you differentiate.

Answer 6

You subtract 1 from the power when you differentiate. You add 1 when you integrate.

Answer 7

ok so lets say is the problem i'm trying to solve for. How would I do it. I think i made a mistake when asking my question. Sorry :(