Exercise
Find the derivative of the following function:
f(x)=x^2\cdot e^{3x}\cdot \ln(2x)
Final Answer
Solution
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:
=2xe^{3x}\ln(2x)+3x^2e^{3x}\ln(2x)+xe^{3x}=
=xe^{3x}(2\ln(2x)+3x\ln(2x)+1)
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