Find the Derivative - d/dy (y^4)/4+1/(8y^2)

Problem

d()/d(y)*((y4)/4+1/(8*y2))

Solution

1. Rewrite the expression using negative exponents to make it easier to apply the power rule.

(y4)/4+1/8*y(−2)

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

d()/d(y)(y4)/4+d()/d(y)1/8*y(−2)

3. Apply the power rule to the first term by multiplying by the exponent and subtracting one from the exponent.

1/4⋅4*y3=y3

4. Apply the power rule to the second term.

1/8⋅(−2)*y(−3)=−1/4*y(−3)

5. Simplify the expression by rewriting the negative exponent as a fraction.

y3−1/(4*y3)

Final Answer

d()/d(y)*((y4)/4+1/(8*y2))=y3−1/(4*y3)

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