f(x) = sin (2x) f’(x) = 2 cos (2x) f(x) = cos (5x 2 ) f’(x) = -10x sin (5x 2 ) f

ID: 2851336 • Letter: F

Question

f(x) = sin (2x)

f’(x) = 2 cos (2x)

f(x) = cos (5x2)

f’(x) = -10x sin (5x2)

f(x) = tan (x2 + 3x)

f’(x) = (2x + 3) sec2 (x2 + 3x)

f(x) = cot (5x2)

f’(x) = -10x csc2 (5x2)

f(x) = csc (2x)

f’(x) = -2csc (2x) cot (2x)

f(x) = sec (x2 + 3x)

f’(x) = (2x + 3) sec (x2 + 3x) tan (x2 + 3x)

What two things do all of the derivatives of the trig functions above have in common?

What do all the derivatives of the functions that start with a c have in common?

How are the derivatives of the cotangent and tangent different than the derivatives of the cosine and sine?

Write the formulas for the derivatives of the secant and the cosecant. Let u be the argument for the trig function.

f(u) = csc (u) f(u) = sec (u)

What do the above formulas have in common?