Question

Differentiate the function b(y) = cy−3 with respect to y. What is the result?

a) b'(y) = c/y⁴
b) b'(y) = -3cy⁻⁴
c) b'(y) = -3cy⁻²
d) b'(y) = -3cy²

Answer 1

The derivative of the function b(y) = cy−3 is found by applying the power rule for differentiation, which results in the derivative being b'(y) = -3cy−´, corresponding to option b).

Step-by-step explanation:

To differentiate the function b(y) = cy−3 with respect to y, we use the power rule for differentiation. The power rule states that if we have a function of the form f(y) = ay^n, where a is a constant coefficient and n is a real number, then the derivative of f with respect to y is f'(y) = an*y^(n-1). Applying this rule to our function:

• Identify the exponent of y, which is -3.
• Multiply the exponent by the constant coefficient c to get the new coefficient: -3c.
• Subtract 1 from the exponent to get the new exponent of y: -3 - 1 = -4.
• The resulting derivative is b'(y) = -3c*y^ (-4), which simplifies to b'(y) = -3cy−´.

The correct answer is b'(y) = -3cy−´, which corresponds to option b).