Posted by stacy on Monday, February 27, 2012 at 12:21am.
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)
Related Questions
COLLEGE CALCULUS. HELP! - Let f(x)=(-3x^2+6)^4(9x^2+7)^14, Find f'(x). f'...
Calculus 12th grade (double check my work please) - 1.)Find dy/dx when y= Ln (...
Calc - Find the derivative of a) y=cos (x/2) b) yx-3x^2 +6 = y^4 + x a) -sin (x/...
Trigonometry - Find the general solution of the following equation. sin (5x) = ...
Math, derivatives - Let g(x) = sin (cos x^3) Find g ' (x): The choices are a...
pre-cal - Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos ...
math calculus - 1.)dy/dx for 3x^7+5/x^3+3(7square roots of x^2)+sinx 2.)d/dx ...
Calculus - Find the dervatives: 1. f(x)=(3x+1)e^x^2 2. y = e^(sin x) ln(x) 3. f(...
calculus - Evaluate the integral of (x)cos(3x)dx A. (1/6)(x^2)(sin)(3x)+C B. (1/...
Calculus AP - Use the table of integrals to find int cos^4 3x dx I found the ...
For Further Reading
