Question

Why is the derivative of (x^2/8) equal to (1/4)x?

Answer 1

\[ \dfrac{x^2}{8} = x^2 \times \dfrac{1}{8}\]Product Rule.

Answer 2

Or even the Power Rule.

Answer 3

\[f(x) = 3x ^{4}-6x ^{3}+\frac{ x ^{2} }{ 8 }+5\]
\[f'(x)=12x ^{3}-18x ^{2}+\frac{ 1 }{ 4 }x\]

How did I get the 1/4? I'm having trouble figuring out how to apply the power rule to fractions.

Answer 4

2/8=1/4

Answer 5

Derp. Thank you!

Answer 6

\[\dfrac{d}{dx} \left( \dfrac{1}{8} x^2 \right)= \dfrac{d}{dx} \left(\dfrac{1}{8} \times 2x\right) = \dfrac{1}{4} x\]