1. ## Derivatives

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)
f'(2) = e^(3(2)^2+2)(6(2))
= (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)
= the number is really large so i dont think this is correct.
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)

2. 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)
Hi surffan,

just a couple of corrections needed.
These curves are very steep for the value of x chosen.