Exercise
$\frac{d}{dx}\left(\frac{x^4}{8}+\frac{1}{4x^2}\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative d/dx((x^4)/8+1/(4x^2)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (\frac{1}{8}) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Multiply the fraction and term in 4\left(\frac{1}{8}\right)x^{3}.
Find the derivative d/dx((x^4)/8+1/(4x^2)) using the sum rule
Final answer to the exercise
$\frac{1}{2}x^{3}+\frac{-1}{2x^{3}}$