Find the Derivative - d/dx y = natural log of 4x^2

Problem

d()/d(x)*ln(4*x2)

Solution

1. Identify the outer function as ƒ(u)=ln(u) and the inner function as u=4*x2

2. Apply the chain rule, which states that d(ln(u))/d(x)=1/u⋅d(u)/d(x)

3. Differentiate the inner function 4*x2 with respect to x using the power rule.

(d(4)*x2)/d(x)=8*x

4. Substitute the components back into the chain rule formula.

d(ln(4*x2))/d(x)=1/(4*x2)⋅8*x

5. Simplify the resulting expression by canceling common factors.

(8*x)/(4*x2)=2/x

Final Answer

d(ln(4*x2))/d(x)=2/x

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