MATH 21 LE 2 DERIVATIVES FUNCTION

Derivative of tan f(x)

• cot^2 f(x) * f'(x)
• sec^2 f(x) * f'(x)
• cos^2 f(x) * f'(x)
• sin^2 f(x) * f'(x)

Derivative of sin f(x)

• sin f(x) * f'(x)
• tan f(x) * f'(x)
• cos f(x) + f'(x)
• cos f(x) * f'(x)

Derivative of cos x

• cos x
• -sin x
• 1
• tan x

Derivative of sec f(x)

• sec f(x) tan f(x)
• 1 / cos f(x)
• cos f(x) / sin f(x)
• sec f(x) / tan f(x)

Derivative of cot f(x)

• sec^2(f(x)) * f'(x)
• sin^2(f(x)) * f'(x)
• csc(f(x)) * f'(x)
• -csc^2(f(x)) * f'(x)

Derivative of csc f(x)

• -csc f(x) tan f(x) f'(x)
• -csc^2 f(x) f'(x)
• -csc f(x) cot f(x)
• -csc f(x) cot f(x) f'(x)

Derivative of Quotient Rule

• (f'g + fg') / g^2
• (f'g - fg') / g
• (f'g - fg) / g
• (f'g - fg') / g^2

Derivative of Product Rule

• u'v + uv'
• u - v
• u + v
• u^2 + v^2

Derivative of Chain Rule

• The derivative of the Chain Rule is (f(g(x)))' = f'(x) * g'(x)
• The derivative of the Chain Rule is (f(g(x)))' = f(x) * g'(x)
• The derivative of the Chain Rule is (f(g(x)))' = f'(g(x))
• The derivative of the Chain Rule is (f(g(x)))' = f'(g(x)) * g'(x)

Derivative of a^x

• x * ln(a)
• a^x + ln(a)
• a^x * ln(a)
• a^(x+1)