What is the Derivative of (x+(3˄x))˄4?

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Answer 1 · 2018-06-16T01:16:00

#dy/dx=4(x+3^x)^3(1+3^xln3)#

.

#y=(x+3^x)^4#

Let #u=x+3^x#

#(du)/dx=1+3^xln3#

#y=u^4#

#dy/(du)=4u^3#

#dy/dx=dy/(du)*(du)/dx#

#dy/dx=4u^3(1+3^xln3)#

Now, we substitute back for #u#:

#dy/dx=4(x+3^x)^3(1+3^xln3)#