How do you find the derivative of #f (x) = x^6 · e^(7x)#?
1 Answer
Jan 21, 2016
Explanation:
Use the product rule, which states that for a function
#f'(x)=g'(x)h(x)+g(x)h'(x)#
We have:
#g(x)=x^6#
#h(x)=e^(7x)#
Find the derivatives of either function.
Through the power rule,
#g'(x)=6x^5#
Through the chain rule, particularly applied to
#h'(x)=e^(7x)d/dx[7x]=7e^(7x)#
Plug both of these into the original equation.
#f'(x)=6x^5e^(7x)+x^6(7e^(7x))#
#f'(x)=x^5e^(7x)(7x+6)#