Calculating Derivative – A multiplication of polynom, ln and e – Exercise 6275


Find the derivative of the following function:

f(x)=x^2\cdot e^{3x}\cdot \ln(2x)

Final Answer



We simplify the function before differentiating:

f(x)=x^2\cdot e^{3x}\cdot \ln(2x)=

=(x^2\cdot e^{3x})\cdot \ln(2x)

Using Derivative formulas and the multiplication rule in Derivative Rules, we get the derivative:

f'(x)=(2xe^{3x}+x^2\cdot 3e^{3x})\ln (2x)+(x^2e^{3x}\cdot\frac{1}{2x}\cdot 2=

One can simplify the derivative:



Have a question? Found a mistake? – Write a comment below!
Was it helpful? You can buy me a cup of coffee here, which will make me very happy and will help me upload more solutions! 

Share with Friends

Leave a Reply