How do you differentiate #f(x)=(x^2+sinx)(e^x-cosx)# using the product rule?

1 Answer
May 18, 2017

Answer:

#f'(x) = x^(2) e^(x) + x^(2) sin(x) + sin(x) e^(x) + sin^(2)(x) + 2 x e^(x) + cos(x) e^(x) - 2 x cos(x) - cos^(2)(x)#

Explanation:

We have: #f(x) = (x^(2) + sin(x))(e^(x) - cos(x))#

#Rightarrow f'(x) = (x^(2) + sin(x)) cdot frac(d)(dx)(e^(x) - cos(x)) + (e^(x) - cos(x)) cdot frac(d)(dx)(x^(2) + sin(x))#

#Rightarrow f'(x) = (x^(2) + sin(x))(e^(x) + sin(x)) + (e^(x) - cos(x))(2 x + cos(x))#

#Rightarrow f'(x) = x^(2) e^(x) + x^(2) sin(x) + sin(x) e^(x) + sin^(2)(x) + 2 x e^(x) + cos(x) e^(x) - 2 x cos(x) - cos^(2)(x)#