Question #01dcb

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Answer 1 · 2017-10-01T15:11:04

# = (-4cos(x)sin(x))/(1+3cos^2x)#

#d/dx(2/3 ln(1 + 3cos^2x)) = 2/3 * (d/dx (ln(1+3cos^2x)))#

(constant pulls out of derivative)

knowing that #d/dx(ln(u)) = 1/u * u'#,

# = 2/3 * 1/ (1+3cos^2x)*d/dx(1+3cos^2x)#

# = 2/(3(1+3cos^2x))*(0 + 3⋅(2cos(x))⋅(-sin(x)))#

# = 2/(3+9cos^2x)*(-6cos(x)sin(x)) = (-12cos(x)sin(x))/(3+9cos^2x)#

# = (-4cos(x)sin(x))/(1+3cos^2x)#