derivative of h(y)=log(y²+4y)
Using the chain rule,
h'(y) = (1/(y²+4y))(2y+4)
h'(y) = (2y+4)/(y²+4y)
To find the derivative of the function h(y) = log(y^2 + 4y), we can use the chain rule.
Step 1: Rewrite the function in a simplified form using the properties of logarithms.
h(y) = log(y^2 + 4y) = log(y(y + 4))
Step 2: Apply the chain rule, which states that if we have a function f(g(y)), the derivative is given by f'(g(y)) * g'(y).
Let's break down the steps and find the derivative:
Step 1: Rewrite the function using the properties of logarithms:
h(y) = log(y(y + 4))
Step 2: Apply the chain rule:
h'(y) = (1 / (y(y + 4))) * (y + 4)
Step 3: Simplify the expression:
h'(y) = (y + 4) / (y(y + 4))
Step 4: Cancel out (y + 4) terms:
h'(y) = 1 / y
So, the derivative of h(y) = log(y^2 + 4y) is h'(y) = 1 / y.