Posted by **stacy** on Monday, February 27, 2012 at 12:21am.

1. If f(x)=sin(x^2), Find f'(x) and f'(1)

2. If d/dx(f(3x^3))=9x^2, Calculate f'(x).

3. Let f(x)=cos(6x+6), find f'(x)

4. Let f(x)=-2sec(2x), find f'(x)

- COLLEGE CALCULUS. HELP! -
**Steve**, Monday, February 27, 2012 at 12:03pm
Looks like an exercise in the chain rule:

f(x) = sin(x^2)

f'(x) = cos(x^2) * 2x = 2x cos(x^2)

f'(1) = 2cos(1)

--------------------

d/dx(f(3x^3))=9x^2

Let g(x) = f(3x^3)

dg/dx = dg/df * df/dx

9x^2 = dg/df * 9x^2

1 = dg/df

Looks like g(x) = x

so, g(f) = f

dg/dx = df/dx = 9x^2

--------------------

f(x)=cos(6x+6)

f' = -sin(6x+6)*6

= -6sin(6x+6)

----------------

f(x)=-2sec(2x)

f' = -2sec(2x)tan(2x)*2

= -2sec(2x)tan(2x)

## Answer This Question

## Related Questions

- Calculus 12th grade (double check my work please) - 1.)Find dy/dx when y= Ln (...
- COLLEGE CALCULUS. HELP! - i dont know how to start this problem. i dont like cos...
- calculus - Find the points on the curve y= (cos x)/(2 + sin x) at which the ...
- Trig - If angle A is 45 degrees and angle B is 60 degrees. Find sin(A)cos(B), ...
- Calculus - ∫((cos^3(x)/(1-sin^(2)) What is the derivative of that integral...
- CALCULUS - If cos(t)=–7/9, find the values of the following trigonometric ...
- Pre-calculus help - I have two problems I am stuck on, if you could show me how ...
- Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...
- Math/Calculus - A series circuit contains a resistor with R = 24 ohms, an ...
- Trig - Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are ...

More Related Questions