Find the Derivative - d/dx (x^4)/4+1/(8x^2)

Problem

d()/d(x)*((x4)/4+1/(8*x2))

Solution

1. Rewrite the expression using negative exponents to make differentiation easier.

(x4)/4+1/8*x(−2)

2. Apply the sum rule for derivatives, which allows for differentiating each term separately.

d()/d(x)(x4)/4+d()/d(x)1/8*x(−2)

3. Apply the power rule d(xn)/d(x)=n*x(n−1) to the first term.

1/4⋅4*x3=x3

4. Apply the power rule to the second term.

1/8⋅(−2)*x(−3)=−1/4*x(−3)

5. Simplify the expression by converting the negative exponent back into a fraction.

x3−1/(4*x3)

Final Answer

d()/d(x)*((x4)/4+1/(8*x2))=x3−1/(4*x3)

Want more problems? Check here!