Find the Derivative - d/dy b(y)=cy^-6

Problem

d()/d(y)*c*y(−6)

Solution

1. Identify the function and the variable of differentiation. The function is b(y)=c*y(−6) where c is a constant and y is the variable.

2. Apply the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of the function.

(d(c)*y(−6))/d(y)=cd(y(−6))/d(y)

3. Apply the power rule, which states that d(yn)/d(y)=n*y(n−1) Here, n=−6

d(y(−6))/d(y)=−6*y(−6−1)

4. Simplify the exponent and the expression.

−6*y(−6−1)=−6*y(−7)

5. Combine the constant c with the result of the power rule.

c*(−6*y(−7))=−6*c*y(−7)

Final Answer

(d(c)*y(−6))/d(y)=−6*c*y(−7)

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