True or false? Provide an example to support your decision. a) The derivative of

Question

True or false? Provide an example to support your decision.
a) The derivative of an even function is even. b) The derivative of an even function is odd. c) The derivative of an odd function is odd. d) The derivative of an odd function is odd.
Please provide a step by step solution for each. Thank you so much for your help. True or false? Provide an example to support your decision.
a) The derivative of an even function is even. b) The derivative of an even function is odd. c) The derivative of an odd function is odd. d) The derivative of an odd function is odd.
Please provide a step by step solution for each. Thank you so much for your help. True or false? Provide an example to support your decision.
a) The derivative of an even function is even. b) The derivative of an even function is odd. c) The derivative of an odd function is odd. d) The derivative of an odd function is odd.
Please provide a step by step solution for each. Thank you so much for your help.

Explanation / Answer

a)false

b)true

f(x) is even ==>f(x)=f(-x) ==>differentiate on bothsides==>f'(x)=-f'(-x) ==>f'(-x)=-f'(x)==>f'(x) is odd

c)false

d)true

f(x) is odd ==>f(x)=-f(-x) ==>differentiate on bothsides==>f'(x)=f'(-x) ==>f'(-x)=f'(x)==>f'(x) is even

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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