Find the Derivative - d/dx e^(3 natural log of x^2)

Problem

d(e(3*ln(x2)))/d(x)

Solution

1. Apply logarithmic properties to simplify the exponent by moving the coefficient inside the natural log as a power.

e(3*ln(x2))=eln((x2)3)

2. Simplify the power inside the natural log using the rule (am)n=a(m*n)

eln((x2)3)=eln(x6)

3. Use the inverse property of the exponential and natural logarithmic functions, where eln(u)=u to simplify the expression before differentiating.

eln(x6)=x6

4. Apply the power rule for differentiation, which states d(xn)/d(x)=n*x(n−1)

d(x6)/d(x)=6*x5

Final Answer

d(e(3*ln(x2)))/d(x)=6*x5

Want more problems? Check here!