How do you use the Product Rule to find the derivative of ##?

Question

1339 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-26T15:22:25

See the explanation.

#h(x)=f(x)*g(x)#

#h'(x)=f'(x)*g(x)+f(x)*g'(x)#

Example:

#h=(x^4-5x^2+1)e^x#

#f=x^4-5x^2+1 => f'=4x^3-10x#
#g=e^x => g'=e^x#

#h'=(4x^3-10x)e^x+(x^4-5x^2+1)e^x#

#h'=(x^4+4x^3-5x^2-10x+1)e^x#