Find y' for y = 2x^4 - sqrt(3)
Find $y'$ for $y = 2x^{4} - \sqrt{3}$.
Explanation of Method
Differentiate a power term together with a constant.
Step 1: Differentiate term by term
Apply the sum–difference rule: $y' = \frac{d}{dx}\!\left(2x^{4}\right) - \frac{d}{dx}\!\left(\sqrt{3}\right)$.
Step 2: Apply the power rule and the constant rule
The number $\sqrt{3}$ is a constant, so its derivative is zero; the power rule gives $(x^{n})' = nx^{n-1}$: \[\frac{d}{dx}\!\left(2x^{4}\right) = 2\cdot 4x^{3} = 8x^{3}, \qquad \frac{d}{dx}\!\left(\sqrt{3}\right) = 0.\]
Step 3: Verification
\[x = 1,\ \Delta x = 10^{-5}:\quad \frac{2(1{+}10^{-5})^{4} - 2\cdot 1^{4}}{10^{-5}} \approx 8.0001 \approx 8 = 8\cdot 1^{3} \;\;\checkmark\]
Result
Final answer:
\[\boxed{\,y' = 8x^{3}\,}\]
Remark
Remark. A constant term never contributes to the derivative: it only shifts the graph up or down without changing its slope. The irrational look of $\sqrt{3}$ is irrelevant — what matters is that it does not depend on $x$.