Using the rules of differentiation, calculate y'

Question

(a) 6√x-4x³ +5e^x

(b) πx²

 

Answer 1

Jason,

 

Just do the differentiation term by term:

 

(a)  y'(x) = 6(1/2)x^(-1/2) - 4(3)x² + 5(e^x)

              = 3 /√x  -  12x² + 5 e^x .

 

(b)  y'(x) = 2nx

Answer 2

Part a

Use the power rule:

 

y=6x^½-4x³+5e^x

 

y'=(3x^-½)-12x²-5e^x

 

Note that the derivative of e^x is e^x.

 

Part b

Use the power rule:

 

y=Πx²

y'=2Πx

 

Note that Π is a constant.