Directions: For each category see if you can devise the rule(s) that was used to

Question

Directions: For each category see if you can devise the rule(s) that was used to find the derivative(s) and then use it to find the derivatives of the functions that follow.

Category 2: Tangent and Cotangent

Function: f(x)=tan?(3x) 3. Function: f(x)=7tan?(x^2)

Derivative: f^' (x)=3?sec?^2 (3x) Derivative: f^' (x)=14x?sec?^2 (x^2)

Function: f(x)=cot?(6x) 4. Function: f(x)=1/3 cot?(2x^3)

Derivative: f^' (x)=-6?csc?^2 (6x) Derivative: f^' (x)=-2x^2 ?csc?^2 (2x^3)

What is the formula for the derivative of Tangent? What about for Cotangent?   

Find the derivatives of the following:

f(x)=1/2 tan(x^4) 2. f(x)=6cot(x^3-2x^2)

Explanation / Answer

Derivative of tanx is (secx)^2 and derivative of cotx is -(cosecx)^2

Now derivative of f(x)=1/2 tan(x^4)
f'(x) = 1/2(sec(x^4))^2*4x^3 = 2x^3*(sec(x^4))^2

and derivative of f(x)=6cot(x^3-2x^2)
f'(x) = -6cosec((x^3-2x^2))^2*(3x^2 - 2) = (12-18x^2)cosec((x^3-2x^2))^2

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.