Find the derivative of the function : y = 2^sin(xpi)

Question

Find the derivative of the function : y = 2^sin(xpi)

 

I get that I have to apply the Chain Rule then the Product Rule:

 

d/dx 2^sin(xpi) * d/dx sin(xpi) * [d/dx pi * x + d/dx x * pi]

2sin(xpi)^{sin(xpi) - 1} * cos(xpi) * [0 + pi]

pi * cos(xpi) * 2sin(xpi)^sin(xpi)

 

Where am I going wrong?

 

#33 on p205

ANSWER: y' = cos(xpi) 2^{sin (xpi)} (pi * ln(2))

Answer 1

d/dx(2^sin(xpi)

 

use the formula---

 

d/dx(a^x)=(a^x)*ln(a)

 

d/dx of the given function---

 

[2^sin(xpi)]*ln(2)*cos(xpi)*pi

 

It is the same thing as given.