- #1

calculusthis

- 12

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k guys.. i'd like to try to figure out how to get to the derrivatives on my own so really just looking for a right or wrong.

1. 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]

f'(2)=13e^14 ... correct?

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

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

f'(3)= [2(3)+3] 2^[3^2+(3)(3)] ln 2

f'(3) = 1 635 339.37 ..... correct?

3) y = xe^(2x)

y' = 2x^2e^(2x) + e^(2x) .... correct?

4) f(x) = 3^x + x^3

f'(x= 3^x ln 3 + 3x^2 .... correct?

5) y= e^-(2x+5)

y' = e^(-2x-5) * (-2) ... correct?

6) y = e^(3x^2-5x+7)

y' = e^(3x^2-5x+7) * (6x-5) ... correct?

If anyone can quickly tell me if these are differentiated correctly it would be very helpful. I'm new to doing this type of work and find myself second guessing most my results.

thanx for any help.

1. 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]

f'(2)=13e^14 ... correct?

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

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

f'(3)= [2(3)+3] 2^[3^2+(3)(3)] ln 2

f'(3) = 1 635 339.37 ..... correct?

3) y = xe^(2x)

y' = 2x^2e^(2x) + e^(2x) .... correct?

4) f(x) = 3^x + x^3

f'(x= 3^x ln 3 + 3x^2 .... correct?

5) y= e^-(2x+5)

y' = e^(-2x-5) * (-2) ... correct?

6) y = e^(3x^2-5x+7)

y' = e^(3x^2-5x+7) * (6x-5) ... correct?

If anyone can quickly tell me if these are differentiated correctly it would be very helpful. I'm new to doing this type of work and find myself second guessing most my results.

thanx for any help.

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