How do you differentiate f(x)=e^(5x^2+x+3) f(x)=e5x2+x+3 using the chain rule?
2 Answers
Explanation:
Using the
color(blue)" chain rule " chain rule
d/dx[f(g(x)) ] = f'(g(x)).g'(x) ddx[f(g(x))]=f'(g(x)).g'(x) and
d/dx(e^x) = e^xddx(ex)=ex f'(x)
= e^(5x^2+x+3) d/dx(5x^2 + x + 3)=e5x2+x+3ddx(5x2+x+3)
= e^(5x^2+x+3)(10x + 1 )=e5x2+x+3(10x+1)
Explanation:
The given equation is
So that means
From chain rule, we have
So, taking for
You can substitute it all to get back the proper answer.