How do you find the derivative of #f (x) = x^6 · e^(7x)#?

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Answer 1 · 2016-01-21T13:33:48

#f'(x)=x^5e^(7x)(7x+6)#

Use the product rule, which states that for a function #f(x)=g(x)h(x)#, the derivative is

#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)#,

#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)#