Chain Rule
f(x) = (3x+1)²
f'(x) = 6*(3x+1) = 18x + 6
f(x) = (7x3 + 1) * (9x2 + 8)
f'(x) = (7x3 + 1) * (18x) + (9x2 + 8) * (21x2)
f(x)= (x²-1)³/ x²+1
f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²
f(x) = cosx
f'(x) = -sinx
f(x) = [ (1-sin(x)) / cos(x)]
f'(x) = (sin(x) - 1) * sec2(x)
f(x) = sin(4x²)
f"(x) = 8xcos(4x²)
f(x) = x² * sin(x)
f'(x) = 2x*sinx+ x²*cosx
f(x) = x / √(x+1)
f'(x) = (x+2) / 2(x+1)3/2
f(x) = sin(2x)
f'(x) = 2cos(2x)
f(x) = (sin(x)cos(x)) / (1/2*sin(x))
f'(x) = -2sinx
f(x) = √(4x3+5)
f'(x) = 6x2 / √(4x3+5)
f(x) = sin(2x)*cos(3x)
f'(x) = 2cos(2x)cos(3x)−3sin(2x)sin(3x)
f(x) = sin(x) / x
f'(x) = (x*cos(x) - sin (x))/x2
f(x) = cos2(2x)
f'(x) = −4cos(2x)sin(2x)= −2sin(4x)
f(x) = sin[(x-1)/(x+1)]
f'(x) = 2/(x+1)2 * cos[(x-1)/(x+1)]
f(x) = sin((3x-1)2)
f'(x) = 6 * (3x-1) * cos((3x-1)2)
f(x) = x2 * tan(4x)
f'(x) = 2x*tan(4x) + 4x2*sec24x
f(x) = tan(x) / x2 + 1
f'(x) = [(x2+1)(sec2x) − (2x)(tanx)] / (x2+1)2
f(x) = arcsec(x)
f'(x) = 1 / |x| √(x² - 1)
f(x) = sin(x) / √(1+x2)
f'(x) = [cos(x) / √(1+x2)] - [x*sin(x) / (1+x2)3/2]
f'(x) = [cos(x)*(1+x2) - (x*sin(x))] / (1+x2)3/2
f(x) = 3tan(√x)
f'(x) =3/2√x * sec²(√x)
f(x) = (x2 + 3x) * sin(√x)
f'(x) = (2x+3)sin(√x) + [ (x2 + 3x)*cos(√x) / (2√x) ]
f(x) = sec(x) / x2
f'(x) = [sec(x) * (x2tanx−2x)] / x4
f(x) = sec(x2-x)
f'(x) = (2x−1) * sec(x2−x)* tan(x2−x)
f(x) = cos(x2) * √(x2+1)
f'(x) = −2xsin(x2)*√(x2+1) + [x*cos(x2) / √(x2+1)]