Originally Posted by

**surffan** There are a couple equations I was trying to find the derivative of, if anyone can tell me if these look right.

**1. If f(x)=e^(3x^2+x), find f'(2)**

f'(x) = e^(3x^2+x)(6x+1)

f'(2) = e^(3(2)^2+2)(6(2)+1)=13e^(14)

= (1.4)(10^7)

**2. Find the slope of the tangent to the function f(x)=2^(x^2+3x) when x=3**

f'(x) = 2^(x^2+3x)ln2(2x+3)

f'(3) = 2^(3^2+3(3))ln2(2(3)+3)=(9ln2)2^(18)

= the number is really large so i dont think this is correct.

The graph is very steep at x=3

**3. Find the derivative of f(x) = sqrt(x)(2x+3)^2**

f'(x) = (x)^(1/2)' (2x+3)^2 + (x)^(1/2)(2x+3)^2'

f'(x) = ((1/2)x^(-1/2)) ((1)(2x+3)^2) +((x)^(1/2)) ((2)(2x+3)(2))

f'(x) = (2x+3)^2/ (1/2)x^(-1/2) + 4x^1/2(2x+3)