Question

Derivative of 2 tan^3(x)+5 csc^4(x) ?

Answer 1

f'(x) = 2[3tan²(x)sec²(x) - 10csc⁴(x)cot(x)]

Explanation:

f' of tan(x) = sec²(x)

f' of csc(x) = -csc(x)cot(x)

General Power Rule: uⁿ = xuⁿ⁻¹ · u'

Step 1: Write equation

2tan³(x) + 5csc⁴(x)

Step 2: Rewrite

2(tan(x))³ + 5(csc(x))⁴

Step 3: Find derivative

d/dx 2(tan(x))³ + 5(csc(x))⁴

• General Power Rule: 2 · 3(tan(x))² · sec²(x) + 5 · 4(csc(x))³ · -csc(x)cot(x)
• Multiply: 6(tan(x))²sec²(x) - 20(csc(x))³csc(x)cot(x)
• Simplify: 6tan²(x)sec²(x) - 20csc⁴(x)cot(x)
• Factor: 2[3tan²(x)sec²(x) - 10csc⁴(x)cot(x)]